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.*;

public class Main {
	static class Point{
		int x, y, zero, minus;
		public Point(int x, int y) {
			this.x = x;
			this.y = y;
			zero = x + y;
			minus = x - y;
		}
		public int manhattan(Point p) {
			int tmpx = Math.abs(this.x - p.x);
			int tmpy = Math.abs(this.y - p.y);
			return tmpx + tmpy;
		}
	}
	public static void main(String args[]) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		Point p[] = new Point[n];
		for(int i = 0; i < n; ++i){
			p[i] = new Point(sc.nextInt(), sc.nextInt());
		}
		sc.close();
		Arrays.sort(p, new Comparator<Point>() {
			public int compare(Point o1, Point o2) {
				int ans = o1.zero - o2.zero;
				return ans;
			}
		});
		Point max = p[n - 1];
		Arrays.sort(p, new Comparator<Point>() {
			public int compare(Point o1, Point o2) {
				int ans = o1.minus - o2.minus;
				return ans;
			}
		});
		int ans = max.manhattan(p[0]);
		System.out.println(ans);
	}
}