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;

int main() {
   int N;
   cin >> N;
   long long X[N],Y[N];
   for (int i=0; i<N; i++) {
       int x,y;
       cin >> x >> y;
       X[i]=x+y;Y[i]=x-y;
   }
   sort(X,X+N);sort(Y,Y+N);
   cout << max(X[N-1]-X[0],Y[N-1]-Y[0]) << endl;
}