Problem:
Score : 500 points

Problem Statement

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.

Sample Input 1

3
1 1
2 4
3 2

Sample Output 1

4

The Manhattan distance between the first point and the second point is |1-2|+|1-4|=4, which is maximum possible.

Sample Input 2

2
1 1
1 1

Sample Output 2

0

Solution in Java (OpenJDK 11.0.6) (judge verdict: Accepted)


import java.util.Scanner;

/**
 * @author kep
 * @date 2020-09-14
 */
public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        long ans = 0;
        long[] max = new long[4];
        long[] min = new long[4];
        for(int i = 0;i<4;i++){
            max[i] = Long.MIN_VALUE;
            min[i] = Long.MAX_VALUE;
        }
        for(int i = 0;i<n;i++){
            long x = scanner.nextLong();
            long y = scanner.nextLong();
            for(int j = 0;j<4;j++){
                long tmp_x = (j >> 1) == 1?-x:x;
                long tmp_y = (j & 1) == 1?-y:y;
                long tmp = tmp_x + tmp_y ;
                min[j] = Math.min(min[j],tmp);
                max[j] = Math.max(max[j],tmp);
                ans = Math.max(ans,max[j]-min[j]);
            }
        }
        System.out.println(ans);
    }
}