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)

fn main() {
    let n: usize = {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        buf.trim_end().parse().unwrap()
    };

    let (mut x, mut y) = (vec![0i64; n], vec![0i64; n]);
    for i in 0..n {
        let mut buf = String::new();
        std::io::stdin().read_line(&mut buf).unwrap();
        let mut iter = buf.split_whitespace();
        x[i] = iter.next().unwrap().parse().unwrap();
        y[i] = iter.next().unwrap().parse().unwrap();
    }

    let ans = {
        [
            (0..n).map(|i| x[i] + y[i]).max().unwrap() -
            (0..n).map(|i| x[i] + y[i]).min().unwrap(),
            (0..n).map(|i| x[i] - y[i]).max().unwrap() -
            (0..n).map(|i| x[i] - y[i]).min().unwrap(),    
            (0..n).map(|i| -x[i] + y[i]).max().unwrap() -
            (0..n).map(|i| -x[i] + y[i]).min().unwrap(),    
            (0..n).map(|i| - x[i] - y[i]).max().unwrap() -
            (0..n).map(|i| - x[i] - y[i]).min().unwrap(),    
        ].iter().max().unwrap().clone()
    };
    println!("{}", ans);
}