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 itertools::Itertools;
fn main() {
    proconio::input! {
        n: usize,
        xys: [(i128, i128); n],
    }
    // |xi - xj| + |yi - yj|
    let xys_pp = xys
        .iter()
        .cloned()
        .sorted_by(|l, r| (l.0 + l.1).cmp(&(r.0 + r.1)))
        .collect_vec();
    let xys_pn = xys
        .iter()
        .cloned()
        .sorted_by(|l, r| (l.0 - l.1).cmp(&(r.0 - r.1)))
        .collect_vec();
    let xys_np = xys
        .iter()
        .cloned()
        .sorted_by(|l, r| (-l.0 + l.1).cmp(&(-r.0 + r.1)))
        .collect_vec();
    let xys_nn = xys
        .iter()
        .cloned()
        .sorted_by(|l, r| (-l.0 - l.1).cmp(&(-r.0 - r.1)))
        .collect_vec();
    fn f(a: &(i128, i128), b: &(i128, i128)) -> i128 {
        (a.0 - b.0).abs() + (a.1 - b.1).abs()
    }
    let ans = *[
        f(&xys_pp[0], &xys_pp[n - 1]),
        f(&xys_pn[0], &xys_pn[n - 1]),
        f(&xys_np[0], &xys_np[n - 1]),
        f(&xys_nn[0], &xys_nn[n - 1]),
    ]
    .iter()
    .max()
    .unwrap();
    println!("{}", ans);
}