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;

fn main() {
    input! {
        n: usize,
        xy: [(usize, usize); n],
    }
    let chebyshev: Vec<_> = xy
        .iter()
        .map(|(x, y)| (x + y, x.max(y) - x.min(y)))
        .collect();
    let x_max = chebyshev
        .iter()
        .max_by(|(ax, _ay), (bx, _by)| ax.cmp(bx))
        .unwrap()
        .0;
    let x_min = chebyshev
        .iter()
        .min_by(|(ax, _ay), (bx, _by)| ax.cmp(bx))
        .unwrap()
        .0;
    let y_max = chebyshev
        .iter()
        .max_by(|(_ax, ay), (_bx, by)| ay.cmp(by))
        .unwrap()
        .1;
    let y_min = chebyshev
        .iter()
        .min_by(|(_ax, ay), (_bx, by)| ay.cmp(by))
        .unwrap()
        .1;
    println!("{}", std::cmp::max(x_max - x_min, y_max - y_min));
}