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::Read;
use std::cmp::max;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

    println!("{}", answer);
}

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let n: usize = iterator.next().unwrap().parse().unwrap();
    let mut points: Vec<(isize, isize)> = Vec::new();
    for _ in 0..n {
        let xi: isize = iterator.next().unwrap().parse().unwrap();
        let yi: isize = iterator.next().unwrap().parse().unwrap();
        points.push((xi, yi));
    }

    let mx0 = points.iter().map(|p| p.0 - p.1).max().unwrap();
    let mn0 = points.iter().map(|p| p.0 - p.1).min().unwrap();
    let mx1 = points.iter().map(|p| p.0 + p.1).max().unwrap();
    let mn1 = points.iter().map(|p| p.0 + p.1).min().unwrap();

    let ans = max(mx0 - mn0, mx1 - mn1);
    ans.to_string()
}