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 proconio::{input, marker::*};

#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};

#[allow(unused_imports)]
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*).unwrap();
    }
}

fn main() {
    input! {
        n: usize,
        xy: [(isize,isize); n],
    }

    let xy = xy
        .into_iter()
        .map(|(x, y)| (x + y, x - y))
        .collect::<Vec<_>>();

    let mut xmx = std::isize::MIN;
    let mut xmn = std::isize::MAX;
    let mut ymx = std::isize::MIN;
    let mut ymn = std::isize::MAX;

    for (x, y) in xy {
        xmx = std::cmp::max(xmx, x);
        xmn = std::cmp::min(xmn, x);
        ymx = std::cmp::max(ymx, y);
        ymn = std::cmp::min(ymn, y);
    }

    println!("{}", std::cmp::max(xmx - xmn, ymx - ymn));
}