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)

#[allow(unused_imports)]
use {
    itertools::Itertools,
    proconio::{fastout, input, marker::*},
    std::cmp::*,
    std::collections::*,
    std::io::Write,
    std::ops::*,
};

macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

#[fastout]
fn main() {
    input! {
        n: usize,
        xy: [(i64, i64); n]
    }
    let mut u = vec![];
    let mut v = vec![];
    for (x, y) in xy {
        u.push(x - y);
        v.push(x + y);
    }
    u.sort();
    v.sort();
    let ans = max(u[n - 1] - u[0], v[n - 1] - v[0]);
    println!("{}", ans);
}