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> a(n), b(n);
  for(int i = 0; i < n; i++){
    ll x, y; cin >> x >> y;
    a[i] = x -y; b[i] = x + y;
  }
  sort(a.begin(), a.end());
  sort(b.begin(), b.end());
  ll ma = a[n-1] - a[0];
  ll mb = b[n-1] - b[0];
  ll ans = max(ma, mb);
  cout << ans << endl;
  return 0;
}
