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(void){
  int n; cin>>n;
  int z1=-2000000000,z2=2000000000,w1=z1,w2=z2;
  for(int i=0; i<n; ++i){
    int x,y; cin>>x>>y;
    z1=max(z1,x+y);
    z2=min(z2,x+y);
    w1=max(w1,x-y);
    w2=min(w2,x-y);
  }
  cout<<max(z1-z2,w1-w2);
  return 0;
}
