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;
use std::cmp;

#[allow(non_snake_case)]
fn main() {
    input! {
        N: usize,
        xy: [(i64, i64); N]
    }

    let mut zmin = std::i64::MAX;
    let mut zmax = std::i64::MIN;
    let mut wmin = std::i64::MAX;
    let mut wmax = std::i64::MIN;

    for (x, y) in xy {
        let z = x + y;
        let w = x - y;

        zmin = cmp::min(z, zmin);
        zmax = cmp::max(z, zmax);
        wmin = cmp::min(w, wmin);
        wmax = cmp::max(w, wmax);
    }

    let ans = cmp::max(zmax - zmin, wmax - wmin);
    println!("{}", ans);
}