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 (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include<stdio.h>
#include <stdlib.h>
 
int main()
{
    int n,ans,i,j,xd,yd,dd;
    int *xtop,*ytop;
    // 整数の入力
    scanf("%d", &n);
    xtop =  (int *)malloc(sizeof(int)*n);
    ytop =  (int *)malloc(sizeof(int)*n);
    for(i=0;i<n;i++){
        scanf("%d %d", &xtop[i],&ytop[i]);
    }
    ans=0;
    for(i=0;i<n-1;i++){
       for(j=i+1;j<n;j++){
          xd = xtop[i]-xtop[j];
          if(xd<0) xd = -xd;
          yd = ytop[i]-ytop[j];
          if(yd<0) yd = -yd;
          if(xd+yd > ans) ans = xd+yd;
       }
    }
    // 出力
    printf("%d\n",ans);
    free(xtop);
    free(ytop);
    return 0;
}