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: Accepted)

using System;
using static System.Console;

namespace abc178
{
    class Program
    {
        static void Main()
        {
            var n = int.Parse(ReadLine());
            var points = new int[n][];
            for (var i = 0; i < n; ++i)
            {
                var xy = ReadLine().Split(' ');
                points[i] = new int[] { int.Parse(xy[0]), int.Parse(xy[1]) };
            }
            WriteLine(DistMax(points));
        }
        static int DistMax(int[][] points)
        {
            var sMin = int.MaxValue;
            var sMax = 0;
            var bsMin = int.MaxValue;
            var bsMax = 0;
            foreach (var point in points)
            {
                sMin = Math.Min(sMin, point[0] + point[1]);
                sMax = Math.Max(sMax, point[0] + point[1]);
                bsMin = Math.Min(bsMin, point[1] - point[0]);
                bsMax = Math.Max(bsMax, point[1] - point[0]);
            }
            return Math.Max(sMax - sMin, bsMax - bsMin);
        }
    }
}