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 <bits/stdc++.h>
using namespace std;

typedef long long ll;
const ll mod=1e9+7;
const ll N=20003;
const ll INF=1e10;

int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(NULL);
	int n;
	cin>>n;
	vector<int> x(n),y(n);
	for(int i=0;i<n;i++){
		int a,b;
		cin>>a>>b;
		x[i]=a+b;
		y[i]=a-b;
	}
	sort(x.begin(),x.end());
	sort(y.begin(),y.end());
	cout<<max(x.back()-x.front(),y.back()-y.front());
}	  
