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;
using System.IO;
class e{
    public static void Main(){
        long n = long.Parse(Console.ReadLine());
        string[] str = Console.ReadLine().Split(' ');
        (long x, long y) p1 = (long.Parse(str[0]), long.Parse(str[1]));
        (long x, long y) p2 = (long.Parse(str[0]), long.Parse(str[1]));
        long ans = Distance(p1, p2);
        for(long i=0; i<n-2; i++){
            string[] line = Console.ReadLine().Split(' ');
            (long x, long y) pos = (long.Parse(line[0]), long.Parse(line[1]));
            long t1 = Distance(pos, p1);
            long t2 = Distance(pos, p2);
            if(t1 > t2){
                if(t1 > ans){
                    ans = t1;
                    p1 = pos;
                }
            }
            else{
                if(t2 > ans){
                    ans = t2;
                    p2 = pos;
                }
            }
        }
        Console.WriteLine(ans);
    }
    public static long Distance((long x, long y) p1, (long x, long y) p2){
        return Math.Abs(p1.x - p2.x) + Math.Abs(p1.y - p2.y);
    }
}