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(unused, non_snake_case, dead_code, non_upper_case_globals)]
use {
    proconio::{marker::*, *},
    std::{cmp::*, collections::*, mem::*},
};

#[fastout]
fn main() {
    input! {//
        n:usize,
        mut xy:[(i64,i64);n],
    }
    // x と t でわけてかんがえる
    xy.sort();

    let mut ans = 0i64;
    let mut xy45 = vec![];
    let mut xy135 = vec![];
    for &(x, y) in xy.iter() {
        xy45.push((x + y, x - y));
        xy135.push((x - y, x + y));
    }
    // dbg!(&xy45);
    xy45.sort();
    xy135.sort();
    let mut a1 = abs(xy45[0].0, xy45[n - 1].0);
    let mut a2 = abs(xy135[0].0, xy135[n - 1].0);
    println!("{}", max(a1, a2));
}
fn abs(i: i64, j: i64) -> i64 {
    return (i - j).abs();
}