There are N points on the 2D plane, i-th of which is located on (x_i, y_i). There can be multiple points that share the same coordinate. What is the maximum possible Manhattan distance between two distinct points?

Here, the Manhattan distance between two points (x_i, y_i) and (x_j, y_j) is defined by |x_i-x_j| + |y_i-y_j|.

Constraints

* 2 \leq N \leq 2 \times 10^5
* 1 \leq x_i,y_i \leq 10^9
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
x_1 y_1
x_2 y_2
:
x_N y_N


Output

Print the answer.

Examples

Input

3
1 1
2 4
3 2


Output

4


Input

2
1 1
1 1


Output

0
import java.util.Arrays;
import java.util.Scanner;
import java.util.stream.IntStream;

public class Main {

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			int n = scanner.nextInt();
			long[] p = new long[n], q = new long[n];
			IntStream.range(0, n).forEach(i -> {
				long x = scanner.nextLong(), y = scanner.nextLong();
				p[i] = x + y;
				q[i] = x - y;
			});
			System.out
					.println(Math.max(Math.abs(Arrays.stream(p).max().getAsLong() - Arrays.stream(p).min().getAsLong()),
							Math.abs(Arrays.stream(q).max().getAsLong() - Arrays.stream(q).min().getAsLong())));
		}
	}
}
