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>
using namespace std;
int a[200005],b[200005],c[200005];
int main(int argc, char** argv) {
	int n;
	cin >> n;
	for(int i=1;i<=n;i++) cin >> a[i] >> b[i];
	int ans=0;
	for(int i=1;i<=n;i++) c[i]=a[i]+b[i];
	sort(c+1,c+n+1);
	ans=max(ans,c[n]-c[1]);
	for(int i=1;i<=n;i++) c[i]=a[i]-b[i];
	sort(c+1,c+n+1);
	ans=max(ans,c[n]-c[1]);
	cout << ans;
	return 0;
}