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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigDecimal;

public class Main {

	/* several useful subroutines */
	private static final BigDecimal BD1000000007 = new BigDecimal(1000000007);
	private static BufferedReader brStdin = new BufferedReader(new InputStreamReader(System.in));
	private static String[] readBuf = null;
	private static int readPtr = 0;
	private static String getString() throws IOException {
		while ( readBuf == null || readPtr >= readBuf.length ) {
			readBuf = brStdin.readLine().split(" ");
			readPtr = 0;
		}
		return readBuf[readPtr++];
	}
	private static int getInt() throws IOException {
		return Integer.parseInt(getString());
	}
	private static long getLong() throws IOException {
		return Long.parseLong(getString());
	}
	private static BigDecimal getBD() throws IOException {
		return new BigDecimal(getString());
	}
	@SuppressWarnings("unused")
	private static String[] getStringArray(int size) throws IOException {
		String stringArray[] = new String[size];
		for (int i = 0; i < stringArray.length; i++) {
			stringArray[i] = getString();
		}
		return stringArray;
	}
	@SuppressWarnings("unused")
	private static int[] getIntArray(int size) throws IOException {
		int intArray[] = new int[size];
		for (int i = 0; i < intArray.length; i++) {
			intArray[i] = getInt();
		}
		return intArray;
	}
	@SuppressWarnings("unused")
	private static long[] getLongArray(int size) throws IOException {
		long longArray[] = new long[size];
		for (int i = 0; i < longArray.length; i++) {
			longArray[i] = getLong();
		}
		return longArray;
	}
	@SuppressWarnings("unused")
	private static BigDecimal[] getBDArray(int size) throws IOException {
		BigDecimal bdArray[] = new BigDecimal[size];
		for (int i = 0; i < bdArray.length; i++) {
			bdArray[i] = getBD();
		}
		return bdArray;
	}
	private static BigDecimal mod1000000007(BigDecimal bd) {
		return bd.subtract(BD1000000007.multiply(bd.divide(BD1000000007, BigDecimal.ROUND_DOWN))) ;
	}
	@SuppressWarnings("unused")
	private static BigDecimal mod1000000007(int i) {
		return mod1000000007(new BigDecimal(i)) ;
	}
	@SuppressWarnings("unused")
	private static BigDecimal mod1000000007(long l) {
		return mod1000000007(new BigDecimal(l)) ;
	}

	
	/* main routine */
	public static void main(String args[]) throws IOException {
		int n = getInt();
		int a[][] = new int[n][n-1];
		for ( int i = 0; i < n ; i++ ) {
			System.arraycopy(getIntArray(n-1), 0, a[i], 0, n-1);
		}
		int p[] = new int[n];
		boolean f[] = new boolean[n];
		for ( int i = 0; i < n ; i++ ) {
			p[i] = 0;
		}
		int day = 1;
		for(;;) {
			boolean nm = true;
			for ( int i = 0; i < n ; i++ ) {
				f[i] = true;
			}
			for ( int i = 0; i < n ; i++ ) {
				if ( f[i] ) {
					if ( p[i] < n-1 ) {
						int j = a[i][p[i]] - 1;
						if ( f[j] && a[j][p[j]] - 1 == i ) {
							nm = false;
							p[i]++;
							p[j]++;
							f[i] = false;
							f[j] = false;
						}
						
					}
				}
			}
			boolean bf = true;
			for ( int i = 0; i < n ; i++ ) {
				if ( p[i] < n-1 ) {
					day++;
					bf = false;
					break;
				}
			}
			if ( bf ) {
				break;
			}
			if ( nm ) {
				day = -1;
				break;
			}
		}
		if ( day > n ) {
			day = -1;
		}
		System.out.println(day);
	}
}