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 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("filed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn main() {
    let n:usize = read();
    let mut x = Vec::new();
    let mut y = Vec::new();
    for i in 0..n {
        x.push((read::<i64>(), i));
        y.push((read::<i64>(), i));
    }
    let xmin = x.iter().min().unwrap();
    let xmax = x.iter().max().unwrap();
    let ymin = y.iter().min().unwrap();
    let ymax = y.iter().max().unwrap();
    if (ymax.0 - ymin.0).abs() > (xmax.0 - xmin.0).abs() {
        println!("{}", (ymax.0 - ymin.0).abs() + (x[ymax.1].0 - x[ymin.1].0).abs());
    } else {
        println!("{}", (xmax.0 - xmin.0).abs() + (y[xmax.1].0 - y[xmin.1].0).abs());
    }
}