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: Wrong Answer)

use proconio::input;
use std::cmp;

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

    let mut max1 = xys[0];
    let mut max2 = xys[0];
    let mut max3 = xys[0];
    let mut max4 = xys[0];

    let (x0, y0) = xys[0];
    for &(x, y) in &xys[1..] {
        if x0 <= x && y0 <= y {
            if dist((x0, y0), max1) < dist((x0, y0), (x, y)) {
                max1 = (x, y);
            }
        } else if x < x0 && y0 <= y {
            if dist((x0, y0), max2) < dist((x0, y0), (x, y)) {
                max2 = (x, y);
            }
        } else if x < x0 && y < y0 {
            if dist((x0, y0), max3) < dist((x0, y0), (x, y)) {
                max3 = (x, y);
            }
        } else {
            if dist((x0, y0), max4) < dist((x0, y0), (x, y)) {
                max4 = (x, y);
            }
        }
    }

    let mut ans = [max1, max2, max3, max4]
        .iter()
        .map(|&p| dist((x0, y0), p))
        .max()
        .unwrap();

    ans = cmp::max(ans, dist(max1, max3));
    ans = cmp::max(ans, dist(max2, max4));
    println!("{}", ans);
}

fn dist((x1, y1): (usize, usize), (x2, y2): (usize, usize)) -> usize {
    cmp::max(x1, x2) - cmp::min(x1, x2) + cmp::max(y1, y2) - cmp::min(y1, y2)
}