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;

#[allow(non_snake_case)]
fn main() {
    input! {
        N: usize,
        mut xy: [(i64, i64); N]
    }

    for i in 0..N {
        let x = xy[i].0;
        let y = xy[i].1;
        xy[i].0 = x - y;
        xy[i].1 = x + y;
    }

    let max = xy
        .iter()
        .max_by_key(|(x, y)| {
            //
            x.abs() + y.abs()
        })
        .unwrap();
    let min = xy
        .iter()
        .min_by_key(|(x, y)| {
            //
            x.abs() + y.abs()
        })
        .unwrap();

    let ans = cmp::max(max.0 - min.0, max.1 - min.1);

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