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.*; 
import java.math.*;
import java.util.*;
 
public class Main {
	static final long MOD = 998244353;
	//static final long MOD = 1000000007;
	static boolean[] visited;
    public static void main(String[] args) throws IOException {
        FastScanner sc = new FastScanner();
        int N = sc.nextInt();
        int[][] games = new int[N+1][N-1];
        for (int i = 1; i <= N; i++) {
        	for (int j = 0; j < N-1; j++) {
        		games[i][j] = sc.nextInt();
        	}
        }
        int[] index = new int[N+1];
        int day = 0;
        int complete = 0;
        while (true) {
        	day++;
            boolean[] updates = new boolean[N+1];
            for (int i = 1; i <= N; i++) {
            	if (updates[i] || index[i]==N-1) {
            		continue;
            	}
            	int m1 = games[i][index[i]];
            	int m2 = games[m1][index[m1]];
            	if (m2 == i) {
            		updates[m1] = true;
            		updates[m2] = true;
            	}
            }
            boolean update = false;
            for (int i = 1; i <= N; i++) {
            	if (updates[i]) {
            		update = true;
                	index[i] += 1;
                	if (index[i]==N-1)
                		complete++;
            	}
            }
            //System.out.println(Arrays.toString(index));
        	if (! update) {
        		System.out.println(-1);
        		return;
        	} else if (complete==N) {
        		System.out.println(day);
        		return;
        	}
        }
    }
    
    public static int[] sort(int[] array) {
    	//Sort an array (immune to quicksort TLE)
		Random rgen = new Random();
		for (int i = 0; i< array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    int temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
		Arrays.sort(array);

		return array;
	}
    
    public static int[][] sort(int[][] array) {
    	//Sort an array (immune to quicksort TLE)
		Random rgen = new Random();
		for (int i = 0; i< array.length; i++) {
		    int randomPosition = rgen.nextInt(array.length);
		    int[] temp = array[i];
		    array[i] = array[randomPosition];
		    array[randomPosition] = temp;
		}
		Arrays.sort(array, new Comparator<int[]>() {
			  @Override
			  public int compare(int[] arr1, int[] arr2) {
				  //Ascending order.
				  return arr1[0]-arr2[0];
			  }
		});
		return array;
	}
    
    static class FastScanner { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastScanner() { 
            br = new BufferedReader(new InputStreamReader(System.in)); 
        } 
  
        String next() { 
            while (st == null || !st.hasMoreElements()) { 
                try { 
                    st = new StringTokenizer(br.readLine());
                } catch (IOException  e) { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() { 
            String str = ""; 
            try { 
                str = br.readLine(); 
            } catch (IOException e) {
                e.printStackTrace(); 
            } 
            return str; 
        }
    }
}

class Node {
	public HashSet<Node> children;
	public int n;
	
	public Node(int n) {
		this.n = n;
		children = new HashSet<Node>();
	}
	
	public void addChild(Node node) {
		children.add(node);
	}
	
	public void removeChild(Node node) {
		children.remove(node);
	}

	/* (non-Javadoc)
	 * @see java.lang.Object#hashCode()
	 */
	@Override
	public int hashCode() {
		return n;
	}

	@Override
	public boolean equals(Object obj) {
		if (! (obj instanceof Node)) {
			return false;
		} else {
			Node node = (Node) obj;
			return (n == node.n);
		}
	}
	
	public String toString() {
		return (this.n+1)+"";
	}
}

class BinaryIndexedTree {
	  public long[] arr;
 
	  public BinaryIndexedTree (int N) {
	    arr = new long[N+1];
	    arr[0] = 0;
	  }
 
	  //add k to the i-th element.
	  public void add(long k, int i) {
	    int node = i+1;
	    while (node < arr.length) {
	      arr[node] += k;
	      node += node & (-node);
	    }
	  }
 
	  //sum up the elements from input[s_i] to input[e_i], from [s_i,e_i).
	  public long sum(int s_i, int e_i) {
	    return sum(e_i) - sum(s_i);
	  }
 
	  public long sum(int i) {
	    long total = 0;
	    int node = i;
	    while (node > 0) {
	      total += arr[node];
	      node -= node & (-node);
	    }
	    return total;
	  }
}

class DSU {
	public int N;
	public int[] parent;
	public int[] rank;
	public int count;
	
	public DSU(int numNodes) {
		N = numNodes;
	    parent = new int[N];
	    rank = new int[N];
	    for (int i = 0; i < N; i++) {
	    	parent[i] = i;
	    	rank[i] = 1;
	    }
	    count = numNodes;
	}
	
	public boolean isConnected(int p, int q) {
	    return root(p) == root(q);
	}
	
	public int root(int p) {
		while (p != parent[p])
			p = parent[p];
	    return p;
	}
	
	//only connect p and q if they are disjointed.
	public void connect(int p, int q) {
		int rootP = root(p);
	    int rootQ = root(q);
	    if (rank[rootP] >= rank[rootQ]) {
	    	parent[rootQ] = rootP;
	    	rank[rootP] += rank[rootQ];
	    } else if (rank[rootQ] > rank[rootP]) {
	    	parent[rootP] = rootQ;
	    	rank[rootQ] += rank[rootP];
	    }
	    count--;
	}
}