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;
using ll = long long;

int main(){
  int n;
  cin >> n;
  vector<ll> d1(n), d2(n);
  int x, y;
  for(int i=0; i<n; ++i){
    cin >> x >> y;
    d1[i] = x+y;
    d2[i] = x-y;
  }
  ll ans = 0;
  sort(d1.begin(),d1.end());
  sort(d2.begin(),d2.end());
  ans = max(d1[n-1] - d1[0], d2[n-1] - d2[0]);
  cout << ans << endl;
}