The Alpine Acres Crest ski company wants to decide where to build its new exclusive Christmas ski slope! The area that the company owns can be modelled as an infinite ~2~-dimensional vertical plane.

Moreover, the skiing company has already built ~N~ potential endpoints for the ski slopes at points ~(x_i, y_i)~ where ~x_i~ represents the horizontal distance from the origin and ~y_i~ represents the vertical distance.

In addition to having built ~N~ potential endpoints, the company also surveyed eager skiers to see what steepness they prefer. The results of the surveys showed that there were ~M~ steepnesses that were popular, with the ~i~-th steepness being represented with the integers ~k_i~ and ~d_i~.

Being the company's loyal planner, you are tasked with finding the number of pairs of endpoints that can be possible slopes. Two points are a possible slope if there is at least ~1~ popular steepness ~i~ such that the two points form a line with a gradient equal to ~\frac{k_i}{d_i}~.

The gradient of a line joined by two points ~(x_1, y_1)~ and ~(x_2, y_2)~ is equal to ~\frac{y_2-y_1}{x_2-x_1}~.

Constraints

~2 \le N \le 10^5~

~1 \le M \le 20~

~1 \le x_i, y_i \le 10^9~

~-10^9 \le k_i, d_i \le 10^9~

All ~x_i~ are distinct.

All ~y_i~ are distinct.

Neither ~k_i~ nor ~d_i~ will be ~0~.

Input Specification

The first line contains two space-separated integers ~N~ and ~M~, the number of possible endpoints and the number of steepnesses respectively.

The next ~N~ lines contain two integers ~x_i~ and ~y_i~, the coordinates of the ~i~-th point.

The final ~M~ lines contain two integers ~k_i~ and ~d_i~, the ~i~-th preferred steepness.

Output Specification

Output one integer, the number of pairs of endpoints that can be possible slopes.

Sample Input

3 4
1 2
4 4
7 1
-1 1
2 1
4 6
-2 2

Sample Output

2

Explanation

The line ~y = \frac{4}{6}x+\frac{8}{6}~ intersects points ~(1, 2)~ and ~(4, 4)~. The points ~(4, 4)~ and ~(7, 1)~ are intersected by the line ~y = -x+8~. Thus, there are two possible slopes.