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.Scanner;

public class Main {
    
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        
        final int N = sc.nextInt();
        
        long maxA = Long.MIN_VALUE;
        long minA = Long.MAX_VALUE;
        long maxB = Long.MIN_VALUE;
        long minB = Long.MAX_VALUE;
        
        for (int i = 0; i < N; i++) {
            long x = sc.nextLong();
            long y = sc.nextLong();
            
            long a = x + y;
            long b = x - y;
            
            if (maxA < a) {
                maxA = a;
            }
            if (a < minA) {
                minA = a;
            }
            if (maxB < b) {
                maxB = b;
            }
            if (b < minB) {
                minB = b;
            }
        }
        
        System.out.println(Math.max(maxA - minA, maxB - minB));
    }
}
