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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Iterator;
import java.util.NoSuchElementException;
import java.util.Stack;

public class Main {

	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		FastScanner fc = new FastScanner();
		
		int n = fc.nextInt();
//		int n = Integer.parseInt(br.readLine());

		int[][] games = new int[n][n - 1];

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

//			String[] tmpArray = br.readLine().split(" ");
			for(int j = 0; j < n - 1; j++){
//				games[i][j] = Integer.parseInt(tmpArray[j]);
				games[i][j] = fc.nextInt();
			}
		}
		
		ArrayList[] edges = new ArrayList[n*(n - 1)/2];
		
		for(int i = 0; i < edges.length; i++){
			edges[i] = new ArrayList<Edge>();
		}
		
		//debug
//		for(int i = 1; i <= n; i++){
//			for(int j = 1; j <= n; j++){
//				if(i == j){
//					System.out.print("x ");
//				}
//				else {
//					System.out.print(MatchID.calcID(i, j, n)+" ");
//				}
//			}
//			System.out.println();
//		}
		
		boolean referenced[] = new boolean[edges.length];
		for(int i = 0; i < n; i++){
			for(int j = 1; j < n - 1; j++){
				int prevID = MatchID.calcID(i + 1, games[i][j - 1], n);
				edges[prevID].add(new Edge(i + 1, games[i][j], n));
				referenced[MatchID.calcID(i + 1, games[i][j], n)] = true;
			}
		}
		
		//debug
//		for(int i = 0; i < edges.length; i++){
//			for(int j = 0; j < edges[i].size(); j++){
//				System.out.println("game "+i+" to "+((Edge)(edges[i].get(j))).to);
//			}
//		}
		
		visited = new boolean[edges.length];
		
		for(int i = 0; i < edges.length && !cycle; i++){
			if(referenced[i]){
//				System.out.println("match "+i+" ignored");
				continue;
			}
			
			Arrays.fill(visited, false);
			
			dfs(edges, i, 1);
			
			break;
		}
		
		if(cycle || maxDepth == 0){
			System.out.println(-1);
		}
		else {
			System.out.println(maxDepth);
		}
	}
	
	static boolean visited[];
	static boolean cycle = false;
	static int maxDepth = 0;

//	static void dfs2(ArrayList<Edge>[] edges, int ID, int depth){
//		Stack<Integer> stack = new Stack<Integer>();
////		if(cycle){
////			return;
////		}
//		visited[ID] = true;
////		maxDepth = Math.max(depth, maxDepth);
//		stack.push(ID);
//		while(!stack.empty()){
//			int tmpID = stack.pop();
//			
//			Iterator<Edge> it = edges[tmpID].iterator();
//			while(it.hasNext()){
//				Edge tmpEdge = it.next();
//
//				if(visited[tmpEdge.to]){
//					cycle = true;
//					break;
//				}
//				else {
//					visited[tmpEdge.to] = true;
//					stack.push(tmpEdge.to);
//				}
//			}
//
//			visited[ID] = false;
//		}
//	}
	
	static void dfs(ArrayList<Edge>[] edges, int ID, int depth){
		if(cycle){
			return;
		}
		visited[ID] = true;
		maxDepth = Math.max(depth, maxDepth);
		if(edges[ID].size() == 0){
			cycle = false;
		}
		boolean hit = false;
		Iterator<Edge> it = edges[ID].iterator();
		while(it.hasNext()){
			Edge tmpEdge = it.next();
			
			if(visited[tmpEdge.to]){
				cycle = true;
				break;
			}
//			else {
			if(!visited[tmpEdge.to]){
				dfs(edges, tmpEdge.to, depth + 1);
				hit = true;
			}
//			}
		}
		
//		if()
		
		visited[ID] = false;
	}
}

class Edge {
	int to;
	
	Edge(int p1, int p2, int n){
		if(p2 > p1){
			int tmp = p2;
			p2 = p1;
			p1 = tmp;
		}
		
		this.to = MatchID.calcID(p1, p2, n);
	}
}

class MatchID {
	static int calcID(int p1, int p2, int n){
		if(p1 > p2){
			int tmp = p2;
			p2 = p1;
			p1 = tmp;
		}
		
		return ((n - 1) + (n - (p1 - 1))) * (p1 - 1)/2 + (p2 - p1) - 1;
		
	}
}

class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;
	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		}else{
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}
	private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
	private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
	public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
	public String next() {
		if (!hasNext()) throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while(isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	public long nextLong() {
		if (!hasNext()) throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while(true){
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			}else if(b == -1 || !isPrintableChar(b)){
				return minus ? -n : n;
			}else{
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
		return (int) nl;
	}
	public double nextDouble() { return Double.parseDouble(next());}
}