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;

int	main(void)
{
	int n;
	cin >> n;
	vector<int> sum(n);
	vector<int> diff(n);
	int x, y;
	for (int i = 0; i < n; i++)
	{
		cin >> x >> y;
		sum[i] = x + y;
		diff[i] = x - y;
	}
	sort(sum.begin(), sum.end());
	sort(diff.begin(), diff.end());
	cout << max((long long)sum[sum.size() - 1] - sum[0], (long long)diff[diff.size() - 1] - diff[0]) << endl;
}