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<iostream>
using namespace std;
int maxv1=-(2e9+5),minv1=2e9+5,maxv2=maxv1,minv2=minv1;
int n;
int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	cin>>n;
	for(int i=1,x,y;i<=n;i++){
		cin>>x>>y;
		maxv1=max(x+y,maxv1);
		minv1=min(x+y,minv1);
		maxv2=max(maxv2,x-y);
		minv2=min(minv2,x-y);
	}
	cout<<max(maxv1-minv1,maxv2-minv2);
} 