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
-dimensional vertical plane.
Moreover, the skiing company has already built
potential endpoints for the ski slopes at points
where
represents the horizontal distance from the origin and
represents the vertical distance.
In addition to having built
potential endpoints, the company also surveyed eager skiers to see what steepness they prefer. The results of the surveys showed that there were
steepnesses that were popular, with the
-th steepness being represented with the integers
and
.
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
popular steepness
such that the two points form a line with a gradient equal to
.
The gradient of a line joined by two points
and
is equal to
.
Constraints




All
are distinct.
All
are distinct.
Neither
nor
will be
.
Input Specification
The first line contains two space-separated integers
and
, the number of possible endpoints and the number of steepnesses respectively.
The next
lines contain two integers
and
, the coordinates of the
-th point.
The final
lines contain two integers
and
, the
-th preferred steepness.
Output Specification
Output one integer, the number of pairs of endpoints that can be possible slopes.
Sample Input
Copy
3 4
1 2
4 4
7 1
-1 1
2 1
4 6
-2 2
Sample Output
Copy
2
Explanation
The line
intersects points
and
. The points
and
are intersected by the line
. Thus, there are two possible slopes.
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