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 itertools::Itertools;
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;

fn main() {
    input! {
        n: usize,
        mut xy: [(i64, i64); n],
    }

    for i in 0..n {
        xy[i] = (xy[i].0 + xy[i].1, xy[i].0 - xy[i].1);
    }

    let mnx = xy.iter().map(|(x, _)| x).min().unwrap();
    let mxx = xy.iter().map(|(x, _)| x).max().unwrap();
    let mny = xy.iter().map(|(_, y)| y).min().unwrap();
    let mxy = xy.iter().map(|(_, y)| y).max().unwrap();

    println!("{}", std::cmp::max(mxx - mnx, mxy - mny));
}