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.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();

        long aMin = Long.MAX_VALUE, aMax = Long.MIN_VALUE;
        long bMin = Long.MAX_VALUE, bMax = Long.MIN_VALUE;
        for(int n=0; n<N; n++){
            long x = sc.nextLong();
            long y = sc.nextLong();

            long a = x-y, b = x+y;
            aMin = Math.min(aMin, a);
            aMax = Math.max(aMax, a);
            bMin = Math.min(bMin, b);
            bMax = Math.max(bMax, b);
        }

        System.out.println(Math.max(aMax-aMin, bMax-bMin));
    }
}