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.

Examples

Input

3
1 1
2 4
3 2


Output

4


Input

2
1 1
1 1


Output

0
#include <bits/stdc++.h>
using namespace std;
 
 
int main() {
  int n;
  scanf("%d",&n);
  int x,y;
  scanf("%d %d",&x,&y);
  int a,b,c,d;
  a=b=x+y;
  c=d=x-y;
  for(int i=2;i<=n;i++) {
    scanf("%d %d",&x,&y);
    a=min(a,x+y);
    b=max(b,x+y);
    c=min(c,x-y);
    d=max(d,x-y);
  }
  printf("%d",max(abs(a-b),abs(c-d)));
  return 0;
}
