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;
  cin >> N;
  int64_t x,y,z,w;
  int64_t max_z=0;
  int64_t min_z=1e10;
  int64_t max_w=-1e10;
  int64_t min_w=1e10;
  for(int i=0;i<N;i++){
    cin >> x >> y;
    z=x+y;
    w=x-y;
    max_z=max(max_z,z);
    min_z=min(min_z,z);
    max_w=max(max_w,w);
    min_w=min(min_w,w);
  }
  cout << max(max_z-min_z,max_w-min_w) << endl;
  return 0;
}
