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>
#include<map>
using namespace std;
typedef long long ll;
const int maxn=5e5+10;

int main()
{
	int n;cin>>n;
	vector<ll> a,b;
	for(int i=1;i<=n;i++){
		ll x,y;cin>>x>>y;
		a.push_back(x+y);b.push_back(x-y);
	}
	sort(a.begin(),a.end());sort(b.begin(),b.end());
	cout<<max(a[n-1]-a[0],b[n-1]-b[0]);
	return 0;	
} 