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)

// -*- coding:utf-8-unix -*-

use proconio::{fastout, input};

#[fastout]
fn main() {
    input! {
        n: usize,
        xy: [(isize, isize); n]
    }
    let mut maxu = -10000000000;
    let mut minu = 10000000000;
    let mut maxv = -10000000000;
    let mut minv = 10000000000;
    for &(x, y) in &xy {
        let u = x + y;
        let v = x - y;
        maxu = maxu.max(u);
        minu = minu.min(u);
        maxv = maxv.max(v);
        minv = minv.min(v);
    }
    println!("{}", (maxu - minu).max(maxv - minv));
}