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# (Mono-csc 3.5.0) (judge verdict: Wrong Answer)


using System;
using System.Collections.Generic;
using System.Linq;

namespace ConsoleApp1
{
	class Program
	{
		static void Main(string[] args)
		{
			var n = int.Parse(Console.ReadLine());

			var initial = Console.ReadLine().Split(' ').Select(input => long.Parse(input)).ToArray();


			var top = (initial[0], initial[1]);
			var bottom = (initial[0], initial[1]);
			var right = (initial[0], initial[1]);
			var left = (initial[0], initial[1]);

			for (int i = 1; i < n; i++)
			{
				var point = Console.ReadLine().Split(' ').Select(input => long.Parse(input)).ToArray();

				if (point[0] < left.Item1)
				{
					left = (point[0], point[1]);
				}
				if (point[0] > right.Item1)
				{
					right = (point[0], point[1]);
				}
				if (point[1] < bottom.Item2)
				{
					bottom = (point[0], point[1]);
				}
				if (point[1] > top.Item2)
				{
					top = (point[0], point[1]);
				}
			}

			var distances = new[]
			{
				(top, bottom),
				(top, right),
				(top, left),
				(bottom, right),
				(bottom, left),
				(right, left)
            };
			Console.WriteLine(distances.Max(pair => calculateDistance(pair.Item1, pair.Item2)));
		}

		private static long calculateDistance((long, long) p1, (long, long) p2)
        {
			return Math.Abs(p1.Item1 - p2.Item1) + Math.Abs(p1.Item2 - p2.Item2);
        }
	}
}