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 <stdio.h>
#include <algorithm>
int n;
long long a, b;
long long x[200000];
long long y[200000];
int main() {
	scanf("%d", &n);
	for (int i = 0; i < n; i++) {
		scanf("%lld%lld", &a, &b);
		x[i] = a + b;
		y[i] = a - b;
	}
	std::sort(x, x + n);
	std::sort(y, y + n);
	a = x[n - 1] - x[0];
	b = y[n - 1] - y[0];
	if (a < b)a = b;
	printf("%lld\n", a);
}