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;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define P pair<ll,ll>

ll INF=LLONG_MAX;

int main(){
  int n;
  cin>>n;
  ll d1=INF*-1,d2=INF*-1,d3=INF,d4=INF;
  rep(i,n){
    ll x,y;
    cin>>x>>y;
    d1=max(x-y,d1);
    d2=max(x+y,d2);
    d3=min(x-y,d3);
    d4=min(x+y,d4);
  }
  ll ans=max(d1-d3,d2-d4);
  cout<<ans<<endl;
}