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;

int main(){
	int64_t N, x, y, p[2], m[2];
	cin>>N>>x>>y;
	p[0] = p[1] = x + y;
	m[0] = m[1] = x - y;
	while(--N){
		cin>>x>>y;
		tie(p[0], p[1]) = minmax({p[0], p[1], x + y});
		tie(m[0], m[1]) = minmax({m[0], m[1], x - y});
	}
	cout<< max(p[1] - p[0], m[1] - m[0]) <<endl;
}
