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: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.util.AbstractCollection;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.LinkedList;
import java.io.InputStream;

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

    static class ELeague {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();
            int[][] a = new int[n][n - 1];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n - 1; j++) {
                    a[i][j] = in.nextInt();
                }
            }

            ELeague.Vertex[][] vs = new ELeague.Vertex[n + 1][n + 1];
            for (int p1 = 1; p1 <= n; p1++) {
                ELeague.Vertex prev = null;
                for (int i = 0; i < n - 1; i++) {
                    int p2 = a[p1 - 1][i];
                    ELeague.Vertex v = new ELeague.Vertex(p1, p2);
                    if (vs[v.p1][v.p2] == null) {
                        vs[v.p1][v.p2] = v;
                    }
                    if (prev != null) {
                        vs[v.p1][v.p2].inDegree++;
                        vs[prev.p1][prev.p2].outgo.add(vs[v.p1][v.p2]);
                    }
                    prev = v;
                }
            }

            LinkedList<ELeague.Vertex> q = new LinkedList<>();
            for (int p1 = 1; p1 <= n; p1++) {
                for (int p2 = 1; p2 <= n; p2++) {
                    if (vs[p1][p2] != null && vs[p1][p2].inDegree == 0) {
                        q.addFirst(vs[p1][p2]);
                    }
                }
            }
            int ret = 1;
            while (!q.isEmpty()) {
                ELeague.Vertex cur = q.pollFirst();
                int changed = 0;
                for (ELeague.Vertex next : cur.outgo) {
                    next.inDegree--;
                    if (next.inDegree == 0) {
                        changed = 1;
                        q.addLast(next);
                    }
                }
                ret += changed;
            }
            for (int p1 = 1; p1 <= n; p1++) {
                for (int p2 = 1; p2 <= n; p2++) {
                    if (vs[p1][p2] != null && vs[p1][p2].inDegree != 0) {
                        out.println(-1);
                        return;
                    }
                }
            }

            out.println(ret);
        }

        private static class Vertex {
            private ArrayList<ELeague.Vertex> outgo = new ArrayList<>();
            private int inDegree;
            private int p1;
            private int p2;

            private Vertex(int p1, int p2) {
                this.p1 = Math.min(p1, p2);
                this.p2 = Math.max(p1, p2);
            }

            public String toString() {
                return "(" + p1 + " : " + p2 + ", inDegree: " + inDegree + ")";
            }

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void println(int i) {
            writer.println(i);
        }

    }
}