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.