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;

public class Main {
    public static void main(String[] args) {
        try (Scanner in = new Scanner(System.in)) {
            int N = in.nextInt();
            int[] x = new int[N];
            int[] y = new int[N];
            for (int i = 0; i < N; i++) {
                x[i] = in.nextInt();
                y[i] = in.nextInt();
            }

            int[] x2 = new int[N];
            int[] y2 = new int[N];
            for (int i = 0; i < N; i++) {
                x2[i] = x[i] + y[i];
                y2[i] = x[i] - y[i];
            }

            Arrays.sort(x2);
            Arrays.sort(y2);

            long min = Math.max(Math.abs(x2[0] - x2[N - 1]), Math.abs(y2[0] - y2[N - 1]));

            System.out.println(min);
        }
    }
}
