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: Wrong Answer)

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long xminx = sc.nextLong();
        long xminy = sc.nextLong();
        long yminx = xminx;
        long yminy = xminy;
        long xmaxx = xminx;
        long xmaxy = xminy;
        long ymaxx = xminx;
        long ymaxy = xminy;

        for (int i=1;i<n;i++) {
            long x = sc.nextLong();
            long y = sc.nextLong();
            if (xminx > x) {
                xminx = x;
                xminy = y;
            }
            if (yminy > y) {
                yminx = x;
                yminy = y;
            }
            if (xmaxx < x) {
                xmaxx = x;
                xmaxy = y;
            }
            if (ymaxy < y) {
                ymaxx = x;
                ymaxy = y;
            }
        }
        long ans = Math.abs(xminx - yminx) + Math.abs(xminy - yminy);
        long ans2 = Math.abs(xminx - xmaxx) + Math.abs(xminy - xmaxy);
        long ans3 = Math.abs(xminx - ymaxx) + Math.abs(xminy - ymaxy);
        long ans4 = Math.abs(yminx - xmaxx) + Math.abs(yminy - xmaxy);
        long ans5 = Math.abs(yminx - ymaxx) + Math.abs(yminy - ymaxy);
        long ans6 = Math.abs(xmaxx - ymaxx) + Math.abs(xmaxy - ymaxy);

        if (ans < ans2) {
            ans = ans2;
        }
        if (ans < ans3) {
            ans = ans3;
        }
        if (ans < ans4) {
            ans = ans4;
        }
        if (ans < ans5) {
            ans = ans5;
        }
        if (ans < ans6) {
            ans = ans6;
        }

        System.out.println(ans);
    }
}