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)

#[allow(unused_imports)]
use proconio::{
    fastout, input,
    marker::{Bytes, Chars, Isize1, Usize1},
};
#[fastout]
fn main() {
    input!(n: usize, xy: [(isize, isize); n]);

    let x_max = xy.iter().map(|x| x.0).max().unwrap();
    let x_min = xy.iter().map(|x| x.0).min().unwrap();
    let y_max = xy.iter().map(|x| x.1).max().unwrap();
    let y_min = xy.iter().map(|x| x.1).min().unwrap();

    let x: Vec<(isize, isize)> = xy
        .into_iter()
        .filter(|x| x.0 == x_max || x.0 == x_min || x.1 == y_max || x.1 == y_min)
        .collect();

    let mut ans = 0;
    for i in 0..x.len() - 1 {
        for j in i + 1..x.len() {
            ans = std::cmp::max(ans, (x[i].0 - x[j].0).abs() + (x[i].1 - x[j].1).abs());
        }
    }

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