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;
long long n;
long long x[1100000],y[1100000],xx[1100000],yy[1100000];
long long ans;
int main()
{
	cin >> n;
	for(int i=1; i<=n; i++)
		cin >> x[i] >> y[i],xx[i] = x[i] + y[i],yy[i] = x[i] - y[i];
	sort(xx + 1, xx + 1 + n);
	ans = xx[n] - xx[1];
	sort(yy + 1, yy + 1 + n);
	ans = max(ans, yy[n] - yy[1]);
	cout << ans << endl;
}