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.*;
public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        final long bill = 2000000000;
        long pos[][] = new long [n][2];
        long neo_pos[][] = new long [n][2];
        long xMax = bill * -1, xMin = bill;
        long yMax = bill * -1, yMin = bill;

        for(int i = 0; i < n; i++){
            pos[i][0] = sc.nextInt();
            pos[i][1] = sc.nextInt();
            //xy座標から座標軸を45度回転させたx'y'座標に変換する
            //本来は√2で割らないといけないが整数計算で処理したいので行わない
            neo_pos[i][0] = pos[i][0] + pos[i][1];
            neo_pos[i][1] = pos[i][0] * -1 + pos[i][1];
            if(xMax < neo_pos[i][0]){
                xMax = neo_pos[i][0];
            }
            if(xMin > neo_pos[i][0]){
                xMin = neo_pos[i][0];
            }
            if(yMax < neo_pos[i][1]){
                yMax = neo_pos[i][1];
            }
            if(yMin > neo_pos[i][1]){
                yMin = neo_pos[i][1];
            }
        }
        //xMax xMin yMax yMinを確認
        //System.out.println("xMax=" + xMax + " xMin=" + xMin);
        //System.out.println("yMax=" + yMax + " yMin=" + yMin);
        
        long dist_x = xMax - xMin;
        long dist_y = yMax - yMin;
        if(dist_x > dist_y){
            System.out.println(dist_x);
        }else{
            System.out.println(dist_y);
        }
    }
}