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: Wrong Answer)

#![allow(unused_imports)]
#![allow(dead_code)]
use std::cmp;
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, LinkedList, VecDeque};

fn main() {
    proconio::input! {
        n: usize,
        mut xy: [(i32, i32); n]
    }
    xy.sort();
    let mut ans = 0;
    let mut prev = xy[0].0;
    let mut ymin = xy[0].1;
    let mut ymax = xy[0].1;
    for p in xy {
        if prev != p.0 {
            ymin -= p.0 - prev;
            ymax += p.0 - prev;
            prev = p.0;
        }
        ans = cmp::max(ans, cmp::max(ymax - p.1, p.1 - ymin));
        ymin = cmp::min(ymin, p.1);
        ymax = cmp::max(ymax, p.1);
        println!("{:?} {}", p, ans);
    }

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