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 <iostream>
#include <cstdlib>
#include <algorithm>
using namespace std;

int main() {
	int n;
	cin>>n;
	long long arr1[n];
	long long arr2[n];
	for(int i=0;i<n;i++){
	    int t1,t2;
	    cin>>t1>>t2;
	    arr1[i] = t1+t2;
	    arr2[i] = t1-t2;
	}
	sort(arr1,arr1+n);
	sort(arr2,arr2+n);
	int op1 = arr1[n-1]-arr1[0];
	int op2 = arr2[n-1]-arr2[0];
	cout<<max(op1,op2)<<endl;
	return 0;
}
