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)]

// language: Rust(1.42.0)
// check available crates on AtCoder at "https://atcoder.jp/contests/language-test-202001"
// My Library Repositry is at "https://github.com/Loptall/sfcpl"

use itertools::*;
use itertools_num::*;
use lazy_static::lazy_static;
use maplit::{btreemap, btreeset, hashmap, hashset};
use num_bigint::{BigInt, BigUint};
use num_complex::Complex;
use num_integer::{binomial, gcd, lcm, multinomial, Integer};
use num_rational::Rational;
use num_traits::{
    clamp, one, pow, zero, Num, NumAssignOps, NumOps, One, Pow, Signed, Unsigned, Zero,
};
use permutohedron::Heap;
use proconio::{
    derive_readable, fastout, input, is_stdin_empty,
    marker::{Bytes, Chars, Isize1, Usize1},
};
use rand::random;
use std::cmp::{
    max, min, Ordering,
    Ordering::{Equal, Greater, Less},
    Reverse,
};
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::convert::TryInto;
use std::fmt;
use std::mem::swap;
use std::num::{NonZeroU32, ParseIntError};
use std::ops::{
    Add, AddAssign, BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign, Div, DivAssign,
    Index, IndexMut, Mul, MulAssign, Neg, Rem, RemAssign, Shl, ShlAssign, Shr, ShrAssign, Sub,
    SubAssign,
};
use std::process::exit;
use std::{f32, f64, i128, i16, i32, i64, i8, isize, u128, u16, u32, u64, u8, usize};

pub use visualize::*;
pub mod visualize {
    use itertools::*;
    pub trait Visualize {
        fn visualize(&self, split: &str);
        fn continuous(&self) {
            self.visualize("");
        }
        fn spaces(&self) {
            self.visualize(" ");
        }
        fn lines(&self) {
            self.visualize("\n");
        }
    }
    macro_rules ! impl_vis_for_sized {($ ($ t : ty ) ,+ ) => {$ (impl Visualize for $ t {fn visualize (& self , _split : & str ) {print ! ("{}" , self ) ; } } ) + } ; }
    impl_vis_for_sized! {usize , u8 , u16 , u32 , u64 , u128 , isize , i8 , i16 , i32 , i64 , i128 , String , & str , char }
    impl<T: std::fmt::Display> Visualize for [T] {
        fn visualize(&self, split: &str) {
            print!("{}", self.iter().join(split));
        }
    }
    #[macro_export]
    macro_rules ! vis {() => {println ! () ; } ; ($ last : expr ; ) => {$ last . lines () ; vis ! () } ; ($ last : expr => ) => {$ last . continuous () ; vis ! () ; } ; ($ last : expr $ (, ) ? ) => {$ last . spaces () ; vis ! () ; } ; ($ first : expr ; $ ($ rest : tt ) * ) => {$ first . lines () ; println ! () ; vis ! ($ ($ rest ) * ) ; } ; ($ first : expr => $ ($ rest : tt ) * ) => {$ first . continuous () ; vis ! ($ ($ rest ) * ) ; } ; ($ first : expr , $ ($ rest : tt ) * ) => {$ first . spaces () ; print ! (" " ) ; vis ! ($ ($ rest ) * ) ; } ; }
}

pub use consts::*;
pub mod consts {
    pub const MOD10E9_7: usize = 1000000007; // 10 ^ 9 + 7
    pub const MOD99_: usize = 998244353;
    pub const MAX: usize = std::usize::MAX; // = 2 ^ 64 - 1 = 18446744073709551615 ≈ 1.8 * 10 ^ 19
    pub const INF: usize = 2000000000000000000; // MAX / 9 < 2 * 10e18 < MAX / 10
    pub const FNI: i64 = -2000000000000000000; // == -(INF as i64)
    pub const PI: f64 = std::f64::consts::PI; // 3.141592653589793 -- 10 ^ -15
    pub const ASCII_A_LARGE: u8 = 65;
    pub const ASCII_A_SMALL: u8 = 97;
    pub const ASCII_0: u8 = 48;
    pub const ADJ4: &[(isize, isize); 4] = &[(1, 0), (0, 1), (-1, 0), (0, -1)];
    pub const ADJ8: &[(isize, isize); 8] = &[
        (1, 0),
        (1, 1),
        (0, 1),
        (-1, 1),
        (-1, 0),
        (-1, -1),
        (0, -1),
        (1, -1),
    ];
}

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

    let mut a = point[0];
    let mut b = point[1];

    for p in point.into_iter().skip(2) {
        if man(a, p) <= man(p, b) {
            if man(a, b) < man(p,b) {
                a = p;
            }
        } else {
            if man(a, b) < man(a, p) {
                b = p;
            }
        }
    }

    let ans = man(a, b);
    vis!(ans);
}

fn man(a: (i64, i64), b: (i64, i64)) -> i64 {
    (a.0 - b.0).abs() + (a.1 - b.1).abs()
}