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<math.h>
#include<algorithm>
typedef long long ll;

using namespace std;

ll n, a, b;
ll x[200005], y[200005], z[200005];

int main() {
	cin >> n;
	for (int i = 0; i < n; i++) {
		cin >> a >> b;
		x[i] = a + b;
		y[i] = a - b;
		z[i] = b - a;
	}
	sort(x, x + n); sort(y, y + n); sort(z, z + n);
	cout << max((x[n - 1] - x[0]), max((y[n - 1] - y[0]), (z[n - 1]-z[0])));
	return 0;
}