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>
#define ll long long
using namespace std;

int main(){
  ll N;
  cin >> N;
  
  ll xpy[N], xmy[N];
  
  for (int i = 0; i < N; i++){
    ll X,Y;
    cin >> X >> Y;
    
    xpy[i] = X+Y;
    xmy[i] = X-Y;
  }
  sort(xpy, xpy+N);
  sort(xmy, xmy+N);
  
  cout << max((xpy[N-1]-xpy[0]),(xmy[N-1]-xmy[0])) << endl;
  
  return 0;
}