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;
const int Mod=1e9+7;
int x[200005],y[200005];
long long dis[200005];
int main(){
	int n;
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		scanf("%d%d",&x[i],&y[i]);
		dis[i]=x[i]+y[i];
	}
	sort(dis+1,dis+1+n);
	long long ans=dis[n]-dis[1];
	for(int i=1;i<=n;i++){
		x[i]=-x[i];
		dis[i]=x[i]+y[i];
	}
	sort(dis+1,dis+1+n);
	cout<<max(ans,dis[n]-dis[1]);
	return 0;
} 
