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 Rust (1.42.0) (judge verdict: Wrong Answer)

use proconio::input;
use std::cmp::max;
const INF: i64 = 2_000_000_000;

fn dist(p: (i64, i64), q: (i64, i64)) -> i64 {
	(p.0 - q.0).abs() + (p.1 - q.1).abs()
}

fn main() {
	input!(n: usize, points: [(i64, i64); n]);

	let mut xmax = (0, 0);
	let mut ymax = (0, 0);
	let mut xmin = (INF, INF);
	let mut ymin = (INF, INF);

	for point in points {
		if point.0 > xmax.0 { xmax = point; }
		if point.1 > ymax.1 { ymax = point; }
		if point.0 < xmin.0 { xmin = point; }
		if point.1 < ymin.1 { ymin = point; }
	}

	let mut maxdist = 0;
	maxdist = max(maxdist, dist(xmax, ymax));
	maxdist = max(maxdist, dist(xmax, ymin));
	maxdist = max(maxdist, dist(xmax, xmin));
	maxdist = max(maxdist, dist(ymax, ymin));
	maxdist = max(maxdist, dist(ymax, xmin));
	maxdist = max(maxdist, dist(ymin, xmin));

	println!("{}", maxdist);
}