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;

const int INF = 1e9 * 2;
int n, x, y, zx = 0, zm = INF, wx = -INF, wm = INF;

int main()
{
	cin >> n;

	for (int i = 0; i < n; i++) {
		cin >> x >> y;

		zx = max(zx, x + y);
		zm = min(zm, x + y);
		wx = max(wx, x - y);
		wm = min(wm, x - y);
	}

	cout << max(zx - zm, wx - wm) << endl;
}
