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<algorithm>
#include<iostream>
#include<cmath>
using namespace std;
const int N=1e6+10;
int a[N],b[N],n,ans;
int main(){
	int n;
	cin>>n;
	for(int i=1;i<=n;i++){
		int x,y;
		cin >> x >> y;
		a[i] = x+y;b[i]=x-y;
	}
	sort(a+1,a+n+1);
	sort(b+1,b+n+1);
	ans = max(a[n]-a[1],b[n]-b[1]);
	cout<<ans<<'\n';
}