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)

use proconio::*;

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

    let mut r_x = Vec::new();
    let mut r_y = Vec::new();
    for (i, &(x, y)) in xy.iter().enumerate() {
        r_x.push((x+y, i));
        r_y.push((x-y, i));
    }

    r_x.sort();
    r_y.sort();

    let x1 = r_x[0].1;
    let x2 = r_x[n-1].1;
    let y1 = r_y[0].1;
    let y2 = r_y[n-1].1;
    let ans = ((xy[x1].0-xy[x2].0).abs() + (xy[x1].1-xy[x2].1).abs())
        .max((xy[y1].0-xy[y2].0).abs() + (xy[y1].1-xy[y2].1).abs());

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