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;
	vector<long long>plus;
	vector<long long>minus;
	while(n--){
		long long x,y;
		cin>>x>>y;
		plus.push_back(x+y);
		minus.push_back(x-y);
	}
	sort(plus.begin(),plus.end());
	sort(minus.begin(),minus.end());
	long long ret = 0;
	ret = max(ret,plus[plus.size()-1]-plus[0]);
	ret = max(ret,minus[minus.size()-1]-minus[0]);
	cout<<ret;
}