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
// E - Dist Max
#include <bits/stdc++.h>
using namespace std;
using ll = int64_t;

int main(){
	int N; cin>>N;
	vector<ll> p, m;
	while(N--){
		ll x, y; cin>>x>>y;
		p.push_back(x + y);
		m.push_back(x - y);
	}
	sort(p.begin(), p.end());
	sort(m.begin(), m.end());
	cout<< max(p.back() - p[0], m.back() - m[0]) <<endl;
}
