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::collections::*;
use std::io::*;
use std::*;
// template {{{
macro_rules! get {
    ($($t:tt),*; $n:expr) => {
        {
            let stdin = std::io::stdin();
            let ret = std::io::BufRead::lines(stdin.lock()).take($n).map(|line| {
                let line = line.unwrap();
                let mut it = line.split_whitespace();
                _get!(it; $($t),*)
            }).collect::<Vec<_>>();
            ret
        }
    };
    ($($t:tt),*) => {
        {
            let mut line = String::new();
            std::io::stdin().read_line(&mut line).unwrap();
            let mut it = line.split_whitespace();
            _get!(it; $($t),*)
        }
    };
}
macro_rules! _get {
    ($it:ident; [char]) => {
        _get!($it; String).chars().collect::<Vec<_>>()
    };
    ($it:ident; [u8]) => {
        _get!($it; String).bytes().collect::<Vec<_>>()
    };
    ($it:ident; usize1) => {
        $it.next().unwrap().parse::<usize>().unwrap_or_else(|e| panic!("{}", e)) - 1
    };
    ($it:ident; [usize1]) => {
        $it.map(|s| s.parse::<usize>().unwrap_or_else(|e| panic!("{}", e)) - 1).collect::<Vec<_>>()
    };
    ($it:ident; [$t:ty]) => {
        $it.map(|s| s.parse::<$t>().unwrap_or_else(|e| panic!("{}", e))).collect::<Vec<_>>()
    };
    ($it:ident; $t:ty) => {
        $it.next().unwrap().parse::<$t>().unwrap_or_else(|e| panic!("{}", e))
    };
    ($it:ident; $($t:tt),+) => {
        ($(_get!($it; $t)),*)
    };
}
// }}}

fn distance(x: (i64, i64), y: (i64, i64)) -> i64 {
    (x.0 - y.0).abs() + (x.1 - y.1).abs()
}
fn main() {
    let n = get!(usize);
    let mut points = get!(i64,i64;n);
    points.sort();
    let xmax = *points.last().unwrap();
    let xmin = points[0];
    let mut points: Vec<_> = points.iter().map(|x| (x.1, x.0)).collect();
    points.sort();
    let ymax = *points.last().unwrap();
    let ymin = points[0];
    let ymax = (ymax.1, ymax.0);
    let ymin = (ymin.1, ymin.0);
    let ans = distance(xmax, xmin)
        .max(distance(xmax, ymax))
        .max(distance(xmax, ymin))
        .max(distance(xmin, ymax))
        .max(distance(xmin, ymin))
        .max(distance(ymax, ymin));
    println!("{}", ans);
}