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)

use proconio::input;

fn main() {
  input! {
    n: usize,
    mut vals: [(isize, isize);n]
  }
  
  let mut xis: Vec<isize> = vec![0;n];
  for i in 0..n {
    xis[i] = vals[i].0 - vals[i].1;
  }
  xis.sort();
  
  let mut xiis: Vec<isize> = vec![0;n];
  for i in 0..n {
    xiis[i] = vals[i].0 + vals[i].1;
  }
  xiis.sort();  
  let result = std::cmp::max(
    xis.last().unwrap() - xis[0],
    xiis.last().unwrap() - xiis[0]
  );
  
  println!("{}", result);
}