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 C# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Linq;

namespace ConsoleApp3
{
    internal class Class2
    {
        private static void Main(string[] args)
        {
            var x = int.Parse(Console.ReadLine());

            var xys = Enumerable.Range(0, x)
                .Select(_ =>
                {
                    var xy = Console.ReadLine().Split(" ").Select(decimal.Parse).ToArray();
                    var x = xy[0];
                    var y = xy[1];
                    return (x, y, all: (xy[0] * xy[0]) + (xy[1] * xy[1]));
                })
                .ToArray();

            var (minX, minY, _) = xys.OrderBy(x => x.all).First();
            var (maxX, maxY, _) = xys.OrderByDescending(x => x.all).First();

            Console.WriteLine(Math.Abs(minX - maxX) + Math.Abs(minY - maxY));
        }
    }
}