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 Pascal (FPC 3.0.4) (judge verdict: Time Limit Exceeded)

program test;
{$mode objfpc}{$H+}{$R+}{$S+}
Uses sysutils;
var
	N,i,j	    :integer;
    X,Y         :array [1..200000] of integer;
	tmp,ans		:integer;
begin
    readln(N);
    for i:=1 to N do if (i<N) then read(X[i],Y[i]) else readln(X[i],Y[i]);

    ans:=0;
    for i:=1 to N-1 do
    begin
        for j:=i+1 to N do
        begin
            tmp:=ABS(X[i]-X[j])+ABS(Y[i]-Y[j]);
            if (ans<tmp) then ans:=tmp;
            tmp:=ABS(X[j]-X[i])+ABS(Y[j]-Y[i]);
            if (ans<tmp) then ans:=tmp;
        end;
    end;
    writeln(stdout,ans);
end.