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(non_snake_case)]
#![allow(unused_imports)]
use proconio::input;
use std::cmp::max;
use std::cmp::min;
use std::collections::HashSet;
// use std::collections::VecDeque;

fn main() {
    input! {
        N: usize,
        XYs: [(i64, i64); N],
    }

    // let set: HashSet<(i64, i64)> = XYs.into_iter().collect();

    // if set.len() == 1 {
    //     println!("0");
    //     return ;
    // }

    // 45度回転
    let mut rotXs: Vec<i64> = vec![0; N];
    let mut rotYs: Vec<i64> = vec![0; N];

    for (i, &(x, y)) in XYs.iter().enumerate() {
        let rotX = x + y;
        let rotY = x - y;

        rotXs[i] = rotX;
        rotYs[i] = rotY;
    }

    rotXs.sort();
    rotYs.sort();

    let max_x = (rotXs[N - 1] - rotXs[0]).abs();
    let max_y = (rotYs[N - 1] - rotYs[0]).abs();
    let ans = max(max_x, max_y);

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