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<int> s,ss;
	for(int i =0; i < n; i++) {
		int x,y; cin >> x >> y;
		s.push_back(x+y);
		ss.push_back(x-y);
	}
	sort(s.begin(), s.end());
	sort(ss.begin(), ss.end());
	cout << max(s[n-1] - s[0],  ss[n-1] - ss[0]) << endl;
	
	return 0;
}
