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>
#define ll long long
using namespace std;
const int maxn=2e5+10;
int d[maxn],f[maxn];
int main(){
	int n,a,b;
	cin>>n;
	for(int i=1;i<=n;i++){
		cin>>a>>b;
		f[i]=a+b;
		d[i]=a-b;
	}
	sort(f+1,f+1+n);
	sort(d+1,d+1+n);
	ll x=max(f[n]-f[1],d[n]-d[1]);
	cout<<x<<endl;
} 