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: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Jaynil
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        ELeague solver = new ELeague();
        solver.solve(1, in, out);
        out.close();
    }

    static class ELeague {
        static int dp[][];
        int ands;

        public boolean dfs(node root, HashSet<node> vis, HashSet<node> res) {
            boolean ans = true;
            if (res.contains(root)) throw new IllegalStateException("loop");
            if (vis.contains(root)) return true;
            vis.add(root);
            res.add(root);
            for (int i = 0; i < root.a.size(); i++) {
                ans = ans & dfs(root.a.get(i), vis, res);
                dp[root.i][root.j] = Math.max(dp[root.i][root.j], 1 + dp[root.a.get(i).i][root.a.get(i).j]);
                ands = Math.max(ands, dp[root.i][root.j]);
            }
            res.remove(root);
            return ans;
        }

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            dp = new int[n][n];
            HashSet<node> vis = new HashSet<>();
            HashSet<node> res = new HashSet<>();
            node st[][] = new node[n][n];
            for (int i = 0; i < n; i++) {
                for (int j = i + 1; j < n; j++) {
                    st[i][j] = new node(i, j);
                }
            }

            for (int i = 0; i < n; i++) {
                int x = in.nextInt() - 1;
                node temp = st[Math.min(i, x)][Math.max(i, x)];
                for (int j = 1; j < n - 1; j++) {
                    int y = in.nextInt() - 1;
                    temp.addEdge(st[Math.min(i, y)][Math.max(i, y)]);
                    temp = st[Math.min(i, y)][Math.max(i, y)];
                }
            }
            for (int i = 0; i < n; i++) {
                for (int j = i + 1; j < n; j++) {
                    if (!vis.contains(st[i][j])) {
                        try {
                            dfs(st[i][j], vis, res);
                        } catch (IllegalStateException e) {
                            out.println(-1);
                            return;
                        }
                    }
                }
            }
            out.println(ands + 1);


        }

        class node {
            List<node> a;
            int i;
            int j;

            node(int i, int j) {
                this.i = i;
                this.j = j;
                a = new ArrayList<>();
            }

            public void addEdge(node x) {
                a.add(x);
            }

        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}