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(dead_code,unused_variables)]
use proconio::{fastout, input};
use std::cmp::max;
const INF : i64 = 1_000_000_007;

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

    let mut a = vec![(0,0),(0,INF),(INF,0),(INF,INF)];
    for i in 0..n{
        for j in 0..4{
            if j==0{
                if v[i] > a[j]{
                    a[j] = v[i];
                }
            }else if j==1{
                if v[i].0 > a[j].0 && v[i].1 < a[j].1{
                    a[j] = v[i];
                }
            }else if j==2{
                if v[i].0 < a[j].0 && v[i].1 > a[j].1{
                    a[j] = v[i];
                }
            }else{
                if v[i] < a[j]{
                    a[j] = v[i];
                }
            }
        }
    }

    let mut ans = 0;
    for i in 0..4{
        for j in 0..n{
            let d = (a[i].0-v[j].0).abs() + (a[i].1-v[j].1).abs();
            ans = max(ans,d);
        }
    }
    
    println!("{}",ans);
}