A9256. Looking for Owls

Emperor Palpatine loves owls very much. The emperor has some blueprints with the new Death Star, the blueprints contain $n$ distinct segments and $m$ distinct circles. We will consider the segments indexed from $1$ to $n$ in some way and the circles — indexed from $1$ to $m$ in some way.

Palpatine defines an owl as a set of a pair of distinct circles $(i,j)$ ( $i<j$ ) and one segment $k$ , such that:

1. circles $i$ and $j$ are symmetrical relatively to the straight line containing segment $k$ ;
2. circles $i$ and $j$ don't have any common points;
3. circles $i$ and $j$ have the same radius;
4. segment $k$ intersects the segment that connects the centers of circles $i$ and $j$ .

Help Palpatine, count the number of distinct owls on the picture.

The first line contains two integers — $n$ and $m$ ( $1<=n<=3·10^{5}$ , $2<=m<=1500$ ).

The next $n$ lines contain four integers each, $x_{1}$ , $y_{1}$ , $x_{2}$ , $y_{2}$ — the coordinates of the two endpoints of the segment. It's guaranteed that each segment has positive length.

The next $m$ lines contain three integers each, $x_{i}$ , $y_{i}$ , $r_{i}$ — the coordinates of the center and the radius of the $i$ -th circle. All coordinates are integers of at most $10^{4}$ in their absolute value. The radius is a positive integer of at most $10^{4}$ .

It is guaranteed that all segments and all circles are dictinct.

Print a single number — the answer to the problem.

Please, do not use the %lld specifier to output 64-bit integers is С++. It is preferred to use the cout stream or the %I64d specifier.

Here's an owl from the first sample. The owl is sitting and waiting for you to count it.