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 int long long
using namespace std;
signed main(){
  int N;
  cin>>N;
  vector<int> A(N),B(N),C(N),D(N);
  for(int i=0;i<N;i++){
    cin>>A[i]>>B[i];
    C[i]=A[i]+B[i];
    D[i]=A[i]-B[i];
  }
  sort(C.begin(),C.end());
  sort(D.begin(),D.end());
  cout<<max(C[N-1]-C[0],D[N-1]-D[0])<<endl;
}