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-mcs 6.8.0.105) (judge verdict: Time Limit Exceeded)

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

namespace AtCoder
{
	class Program
	{
		static void Main(string[] args)
		{
			var N = ReadLineInt();
			var x = new List<long>();
			var y = new List<long>();
			for (int i = 0; i < N; i++)
			{
				var xy = ReadLineLongSplit();
				x.Add(xy[0]);
				y.Add(xy[1]);
			}

			long maxDis = 0;
			for (int i = 0; i < N-1; i++)
			{
				for (int j = i+1; j < N; j++)
				{
					long ans = Math.Abs(x[i]-x[j])+Math.Abs(y[i]-y[j]);
					if (ans > maxDis) maxDis = ans;
				}
			}

			Console.WriteLine(maxDis);
		}

		public static long Gcd(long a, long b)
		{
			if (a < b) return Gcd(b, a);
			while (b != 0)
			{
				var remainder = a % b;
				a = b;
				b = remainder;
			}
			return a;
		}

		public static int nCm(int n, int m)
		{
			if (n == 0) return 0;
			if (m == 0) return 1;
			return n * nCm(n - 1, m - 1) / m;
		}

		public static string ReadLine()
		{
			return Console.ReadLine();
		}

		public static int ReadLineInt()
		{
			return int.Parse(ReadLine());
		}

		public static long ReadLineLong()
		{
			return long.Parse(ReadLine());
		}

		public static string[] ReadLineStringSplit(char s = ' ')
		{
			return ReadLine().Split(s).ToArray();
		}

		public static int[] ReadLineIntSplit(char s = ' ')
		{
			return ReadLine().Split(s).Select(x => int.Parse(x)).ToArray();
		}

		public static long[] ReadLineLongSplit(char s = ' ')
		{
			return ReadLine().Split(s).Select(x => long.Parse(x)).ToArray();
		}
	}
}