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)

#![allow(clippy::needless_range_loop)]
#![allow(unused_macros)]
#![allow(dead_code)]
#![allow(unused_imports)]

use itertools::Itertools;
use proconio::input;
use proconio::marker::*;
use std::collections::BTreeSet;

fn main() {
    input! {
        p: [(isize, isize)]
    }
    let ans = 0;

    let mut s = BTreeSet::new();

    for &(x, y) in &p {
        s.insert(x + y);
    }

    let ans = std::cmp::max(ans, s.iter().rev().next().unwrap() - s.iter().next().unwrap());

    let mut s = BTreeSet::new();

    for &(x, y) in &p {
        s.insert(-x + y);
    }

    let ans = std::cmp::max(ans, s.iter().rev().next().unwrap() - s.iter().next().unwrap());

    let mut s = BTreeSet::new();

    for &(x, y) in &p {
        s.insert(x - y);
    }

    let ans = std::cmp::max(ans, s.iter().rev().next().unwrap() - s.iter().next().unwrap());

    let mut s = BTreeSet::new();

    for &(x, y) in &p {
        s.insert(-x - y);
    }

    let ans = std::cmp::max(ans, s.iter().rev().next().unwrap() - s.iter().next().unwrap());
    println!("{}", ans);
}