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;
#define MOD 1000000007

int main() {
  
  
  int N;
  cin >> N;

  vector<long long> X(N),Y(N);
  vector<long long> x(0),y(0);
  for(int i = 0;i < N;i++) {
    cin >> X[i] >> Y[i];
    x.push_back(X[i]+Y[i]);
    y.push_back(X[i]-Y[i]);
  }

  sort(x.begin(),x.end());
  sort(y.begin(),y.end());

  cout << max(x[N-1]-x[0],y[N-1]-y[0]) << endl;


}
