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(non_snake_case)]
#![allow(unused_imports)]
#![allow(dead_code)]

use proconio::{input, fastout};
use proconio::marker::*;
use whiteread::parse_line;
use std::collections::*;
use num::*;
use num_traits::*;
use superslice::*;
use std::ops::*;

use itertools::Itertools;
use itertools_num::ItertoolsNum;

#[fastout]
fn solve() {
    const MOD: usize = 1_000_000_007;
    const INF: isize = std::isize::MAX;
    
    input!{
        n: usize,
        xy_vec: [(isize, isize); n]
    }

    let mut min_idx = 0;
    let mut max = INF;

    for i in 0..n {
        let (x, y) = xy_vec[i];
        if x + y < max {
            min_idx = i;
            max = x + y;
        }
    }

    let mut min_ans = 0;
    for i in 0..n {
        let (fx, fy) = xy_vec[min_idx];
        let (x, y) = xy_vec[i];
        let mdist = (fx - x).abs() + (fy - y).abs();
        min_ans = std::cmp::max(mdist, min_ans);
    }

    let mut max_idx = 0;
    let mut min = 0;

    for i in 0..n{
        let (x, y) = xy_vec[i];
        if x + y > min {
            max_idx = i;
            min = x + y;
        }
    }

    let mut max_ans = 0;
    for i in 0..n {
        let (fx, fy) = xy_vec[max_idx];
        let (x, y) = xy_vec[i];
        let mdist = (fx - x).abs() + (fy - y).abs();
        max_ans = std::cmp::max(mdist, max_ans);
    }

    let (max_x, max_y) = xy_vec[max_idx];
    let (min_x, min_y) = xy_vec[min_idx];
    println!("{}", (min_x - max_x).abs() + (min_y - max_y).abs())
}

fn main() {
    solve()
}

#[cfg(test)]
mod test {
    use super::solve;
}