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;
using P = pair<int,int>;
#define rep(i,s,n) for(int i = s; i < (int)(n); i++)

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