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<iostream>
#include<vector>
using namespace std;

int main() {
  int N,i,x,y,maxz=-2e9,minz=2e9,maxw=-2e9,minw=2e9;
  cin>>N;
  vector<int> A(N);
  for (i=0;i<N;i++) {
    cin>>x>>y;
    maxz = max(maxz, x+y);
    minz = min(minz, x+y);
    maxw = max(maxw, x-y);
    minw = min(minw, x-y);
  }
  cout<<max(maxz - minz, maxw - minw)<<endl;
  return 0;
}
