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 std::io::*;
use std::str::FromStr;

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("faild to read char") as char)
        .take_while(|c| !c.is_whitespace())
        .collect();
    token
        .parse()
        .ok()
        .expect("faild to parse token")
}

struct Point {
    x: i64,
    y: i64,
}

fn main(){
    let n: usize = read();
    let mut p: Vec<Point> = (0..n).map(|_| Point {x: read(), y: read()}).collect();
    p.sort_by(|a, b| (a.x + a.y).partial_cmp(&(b.x + b.y)).unwrap());
    let plus = (p[0].x - p[n - 1].x).abs() + (p[0].y - p[n - 1].y).abs();
    p.sort_by(|a, b| (a.x - a.y).partial_cmp(&(b.x - b.y)).unwrap());
    let minus = (p[0].x - p[n - 1].x).abs() + (p[0].y - p[n - 1].y).abs();
    println!("{}", std::cmp::max(plus, minus));
}