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;

fn main() {
    input! {
        n: usize,
        xy: [(i64, i64);n],
    };
    let mut dir1max = xy[0].0 + xy[0].1;
    let mut dir1min = xy[0].0 + xy[0].1;
    let mut dir2max = xy[0].0 - xy[0].1;
    let mut dir2min = xy[0].0 - xy[0].1;
    let mut dirmax = 0;
    for i in 1..n {
        let dir1 = xy[i].0 + xy[i].1;
        let dir2 = xy[i].0 - xy[i].1;

        let d = (dir1 - dir1max).abs();
        if d > dirmax { dirmax = d; }
        let d = (dir1 - dir1min).abs();
        if d > dirmax { dirmax = d; }
        let d = (dir2 - dir2max).abs();
        if d > dirmax { dirmax = d; }
        let d = (dir2 - dir2min).abs();
        if d > dirmax { dirmax = d; }

        if dir1 > dir1max {
            dir1max = dir1;
        }
        if dir1 < dir1min {
            dir1min = dir1;
        }
        if dir2 > dir2max {
            dir2max = dir2;
        }
        if dir2 < dir2min {
            dir2min = dir2;
        }
    }
    println!("{}", dirmax);
}