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>
#include<algorithm>
#include<vector>
using namespace std;
int N;
int f(vector<int>A)
{
	sort(A.begin(),A.end());
	return A[A.size()-1]-A[0];
}
int main()
{
	cin>>N;
	vector<int>X(N),Y(N);
	for(int i=0;i<N;i++)
	{
		int x,y;cin>>x>>y;
		X[i]=x+y;
		Y[i]=x-y;
	}
	cout<<max(f(X),f(Y))<<endl;
}
