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 System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Math;

class MainClass : Scanner
{
    static void Main()
    {
        int N = RInt();
        var xy = new long[N][];
        for (int i = 0; i < N; i++)
        {
            xy[i] = RLongs();
        }
        Array.Sort(xy, (a, b) => a[0].CompareTo(b[0]));
        (long x,long y) lu = (xy[0][0], xy[0][1]);
        (long x,long y) rd = (xy[N - 1][0], xy[N - 1][1]);
        for (int i = 0; i < N; i++)
        {
            var pos = xy[i];
            long diflu = ( pos[0]-lu.x) + (pos[1] - lu.y);
            long difrd = (rd.x-pos[0] ) + (rd.y - pos[1]);
            if (diflu > 0) lu = (pos[0], pos[1]);
            else if (difrd > 0) rd = (pos[0], pos[1]);
        }
        (long x, long y) lu2 = (xy[0][0], xy[0][1]);
        (long x, long y) rd2 = (xy[N - 1][0], xy[N - 1][1]);
        for (int i = 0; i < N; i++)
        {
            var pos = xy[i];
            long diflu = (-pos[0] + lu2.x) + (pos[1] - lu2.y);
            long difrd = (-rd2.x + pos[0]) + (rd2.y - pos[1]);
            if (diflu > 0) lu2 = (pos[0], pos[1]);
            else if (difrd > 0) rd2 = (pos[0], pos[1]);
        }
        var ans1 = Abs(lu.x - rd.x) + Abs(lu.y - rd.y);
        var ans2 = Abs(lu2.x - rd2.x) + Abs(lu2.y - rd2.y);
        WriteLine(Max(ans1,ans2));
    }
}



class Scanner
{
    public static string RString() => Console.ReadLine();
    public static int RInt() => ReadTuple<int>();
    public static long RLong() => ReadTuple<long>();
    public static double RDouble() => ReadTuple<double>();

    public static string[] RStrings() => Console.ReadLine().Split();
    public static int[] RInts() => Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
    public static long[] RLongs() => Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
    public static double[] RDoubles() => Array.ConvertAll(Console.ReadLine().Split(), double.Parse);
    public static int[] RInts(Func<string, int> func) => Console.ReadLine().Split().Select(func).ToArray();
    public static long[] RLongs(Func<string, long> func) => Console.ReadLine().Split().Select(func).ToArray();
    public static double[] RDoubles(Func<string, double> func) => Console.ReadLine().Split().Select(func).ToArray();
    //public static string[] RStrings(Func<string, string> func) => Console.ReadLine().Split().Select(func).ToArray();

    public static T1 ReadTuple<T1>()
    {
        var r = RString();
        var r1 = (T1)Convert.ChangeType(r, typeof(T1));
        return r1;
    }
    public static (T1, T2) ReadTuple<T1, T2>()
    {
        var r = RStrings();
        var r1 = (T1)Convert.ChangeType(r[0], typeof(T1));
        var r2 = (T2)Convert.ChangeType(r[1], typeof(T2));
        return (r1, r2);
    }
    public static (T1, T2, T3) ReadTuple<T1, T2, T3>()
    {
        var r = RStrings();
        var r1 = (T1)Convert.ChangeType(r[0], typeof(T1));
        var r2 = (T2)Convert.ChangeType(r[1], typeof(T2));
        var r3 = (T3)Convert.ChangeType(r[2], typeof(T3));
        return (r1, r2, r3);
    }
    public static (T1, T2, T3, T4) ReadTuple<T1, T2, T3, T4>()
    {
        var r = RStrings();
        var r1 = (T1)Convert.ChangeType(r[0], typeof(T1));
        var r2 = (T2)Convert.ChangeType(r[1], typeof(T2));
        var r3 = (T3)Convert.ChangeType(r[2], typeof(T3));
        var r4 = (T4)Convert.ChangeType(r[3], typeof(T4));
        return (r1, r2, r3, r4);
    }
}