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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.util.*;import java.io.*;import java.math.*;
public class Main{
  //↓見なくていいよ！ここから------------------------------------------
  static class InputIterator{
    ArrayList<String> inputLine = new ArrayList<String>(1024);
    int index = 0; int max;
    InputIterator(){
      BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
      while(true){
        String read;
        try{
          read = br.readLine();
        }catch(IOException e){
          read = null;
        }
        if(read != null){
          inputLine.add(read);
        }else{
          break;
        }
      }
      max = inputLine.size();
    }
    boolean hasNext(){return (index < max);}
    String next(){
      if(hasNext()){
        String returnStr = inputLine.get(index);
        index++;
        return returnStr;
      }else{
        throw new IndexOutOfBoundsException("これ以上入力はないよ");
      }
    }
  }
  
  static InputIterator ii = new InputIterator();//リアクティブでは使えないので諦めてScanner使うこと
  static PrintWriter out = new PrintWriter(System.out);
  static void flush(){out.flush();}
  static void myout(Object t){out.println(t);}
  static void myerr(Object t){System.err.print("debug:");System.err.println(t);}
  static String next(){return ii.next();}
  static int nextInt(){return Integer.parseInt(next());}
  static long nextLong(){return Long.parseLong(next());}
  static ArrayList<String> nextStrArray(){return myHanSpSplit(next());}
  static ArrayList<String> myHanSpSplit(String str){return new ArrayList<String>(Arrays.asList(str.split(" ")));}
  static ArrayList<String> nextCharArray(){return mySingleSplit(next());}
  static ArrayList<String> mySingleSplit(String str){return new ArrayList<String>(Arrays.asList(str.split("")));}
  static ArrayList<Integer> nextIntArray(){
    ArrayList<Integer> ret = new ArrayList<Integer>();
    ArrayList<String> input = nextStrArray();
    for(int i = 0; i < input.size(); i++){
      ret.add(Integer.parseInt(input.get(i)));
    }
    return ret;
  }
  static ArrayList<Long> nextLongArray(){
    ArrayList<Long> ret = new ArrayList<Long>();
    ArrayList<String> input = nextStrArray();
    for(int i = 0; i < input.size(); i++){
      ret.add(Long.parseLong(input.get(i)));
    }
    return ret;
  }
  static String kaigyoToStr(String[] list){return String.join("\n",list);}
  static String kaigyoToStr(ArrayList<String> list){return String.join("\n",list);}
  static String hanSpToStr(String[] list){return String.join(" ",list);}
  static String hanSpToStr(ArrayList<String> list){return String.join(" ",list);}
  public static void main(String[] args){
    Runtime rt = Runtime.getRuntime();
    long mae = System.currentTimeMillis();
    solve();
    flush();
    long ato = System.currentTimeMillis();
    myerr("time : " + (ato - mae) + "ms");
    myerr("memory : " + ((rt.totalMemory() - rt.freeMemory()) / 1024) + "KB");
  }
  //↑見なくていいよ！ここまで------------------------------------------
  static void solve(){//ここがメイン関数代わり
	int N = nextInt();
	Node[] list = new Node[N + 1];
	for(int i = 0; i < N; i++){
		list[i + 1] = new Node();
		list[i + 1].next = nextIntArray();
	}
	int count = 0;
	HashSet<Integer> end = new HashSet<Integer>();
	while(true){
		HashSet<Integer> battled = new HashSet<Integer>();
		boolean isBattled = false;
		for(int i = 1; i <= N; i++){
			if(end.contains(i) || battled.contains(i)){
				continue;
			}
			int aite = list[i].next.get(list[i].lastIndex);
			if(!battled.contains(aite) && !end.contains(aite)){
				if(list[aite].next.get(list[aite].lastIndex) == i){
					list[i].lastIndex++;
					list[aite].lastIndex++;
					battled.add(i);
					battled.add(aite);
					if(list[i].lastIndex >= N - 1){
						end.add(i);
					}
					if(list[aite].lastIndex >= N - 1){
						end.add(aite);
					}
					isBattled = true;
				}
			}
		}
		if(!isBattled){
			if(end.size() == N){
				myout(count);
			}else{
				myout(-1);
			}
			return;
		}
		count++;
	}
  }
  //Method addition frame start
static class Node{
	ArrayList<Integer> next;
	int lastIndex = 0;
	Node(){}
}
  //Method addition frame end
}