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_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::ops::Bound::*;
use itertools::Itertools;
use num_traits::clamp;
use ordered_float::OrderedFloat;
use proconio::{input, marker::*, fastout};
use superslice::*;

#[fastout]
fn main() {
    input! {
        n: usize,
        xy: [(i64, i64); n]
    }

    let mut xs = Vec::new();
    let mut ys = Vec::new();
    for (x, y) in xy {
        xs.push(x - y);
        ys.push(x + y);
    }
    let mut xmax = -1i64<<60;
    let mut xmin = 1i64<<60;
    for &x in &xs {
        xmax = max(xmax, x);
        xmin = min(xmin, x);
    }
    let mut ymax = -1i64<<60;
    let mut ymin = 1i64<<60;
    for &y in &ys {
        ymax = max(ymax, y);
        ymin = min(ymin, y);
    }
    let ans = max(xmax - xmin, ymax - ymin);
    println!("{}", ans);

}