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<cstdio>
#include<iostream> 
using namespace std;

int main() {
	int n, u1, v1, u2, v2, x, y, ans;
	cin>>n>>x>>y;
	u1=v1=x+y;
	u2=v2=x-y;
	while(--n){
		cin>>x>>y;
		u1=min(u1,x+y);
		v1=max(v1,x+y);
		u2=min(u2,x-y);
		v2=max(v2,x-y);
	}
	ans=max(v1-u1, v2-u2);
	cout<<ans<<endl;
	return 0;
}
