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, fastout};
use proconio::marker::{Chars};
use proconio::marker::Usize1;
use std::cmp::*;

macro_rules! debug {
      ($($a:expr),*) => {
          eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
    }
}

#[fastout]
fn main() {
    input!{
        n: usize,
    }

    let mut x: Vec<usize> = Vec::new();
    let mut y: Vec<usize> = Vec::new();
    let mut a: Vec<i64> = Vec::new();
    let mut b: Vec<i64> = Vec::new();
    for i in 0..n {
        input!{
            x_tmp: usize,
            y_tmp: usize,
        }
        x.push(x_tmp);
        y.push(y_tmp);
    }

    for i in 0..n {
        a.push(x[i] as i64 - y[i] as i64);
        b.push(x[i] as i64 + y[i] as i64);
    }

    a.sort();
    b.sort();

    println!("{}", max((a[0] - a[n-1]).abs(),
                       (b[0] - b[n-1]).abs()));

}