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;
#define rep(i,n) for(int i =0;i<n;i++)
#define ALL(a) a.begin(),a.end()
typedef long long int ll;
int main(){
  int n;cin >>n;vector<ll> x(n),y(n),z(n),w(n);
  rep(i,n) cin >> x[i] >> y[i];
  rep(i,n){
    z[i]=x[i]+y[i];w[i] = x[i]-y[i];
  }sort(ALL(z));sort(ALL(w));
  cout << max(z[n-1]-z[0],w[n-1]-w[0])<<endl;
}