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;
#define ll long long 
 
 
int main() 
{
 
	int n; cin>>n;
	ll a[n], b[n];
	for(int i = 0; i<n; i++) 
	{
		int x, y; cin>>x>>y;
		a[i] = x+y;
		b[i] = x-y;
	}
	sort(a, a+n);
	sort(b, b+n);
	ll res = abs( a[n-1]-a[0] );
	res = max(res, abs( b[n-1]-b[0] ) );
	cout<<res<<endl;
}