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 proconio::input;

#[allow(unused_macros)]
macro_rules! chmax {
    ($a:expr, $b:expr) => {$a = std::cmp::max($a, $b)}
}

#[allow(unused_macros)]
macro_rules! chmin {
    ($a:expr, $b:expr) => {$a = std::cmp::min($a, $b)}
}

fn main() {
    input! {
        n: usize,
        p: [(i64, i64); n],
    }

    let (x, y) = p[0];
    let mut mx1 = x + y;
    let mut mn1 = x + y;
    let mut mx2 = x - y;
    let mut mn2 = x - y;

    for (x, y) in p {
        chmax!(mx1, x + y);
        chmin!(mn1, x + y);
        chmax!(mx2, x - y);
        chmin!(mn2, x - y);
    }
    let ans = std::cmp::max(mx1 - mn1, mx2 - mn2);
    println!("{}", ans);
}