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: Accepted)

#[allow(unused_imports)] use proconio::{input, marker::{Bytes, Chars, Usize1, Isize1}};
#[allow(unused_imports)] use std::cmp::{min, max};
#[allow(unused_imports)] use superslice::Ext as _;

#[proconio::fastout]
fn main() {
	input! {
		n: usize,
		a: [(isize, isize); n],
	}
	let inf = 999999999999999999isize;

	let mut zmax = -inf;
	let mut zmin = inf;
	let mut wmax = -inf;
	let mut wmin = inf;
	for i in 0..n {
		let x = a[i].0;
		let y = a[i].1;
		zmax = max(zmax, x+y);
		zmin = min(zmin, x+y);
		wmax = max(wmax, x-y);
		wmin = min(wmin, x-y);
	}

	println!("{}", max(zmax-zmin,wmax-wmin));
}