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D. Looking for Owls
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Input

The first line contains two integers — n and m (1 ≤ n ≤ 3·105, 2 ≤ m ≤ 1500).

The next n lines contain four integers each, x1, y1, x2, y2 — 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, xi, yi, ri — the coordinates of the center and the radius of the i-th circle. All coordinates are integers of at most 104 in their absolute value. The radius is a positive integer of at most 104.

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

Output

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.

Examples
Input
1 2
3 2 3 -2
0 0 2
6 0 2
Output
1
Input
3 2
0 0 0 1
0 -1 0 1
0 -1 0 0
2 0 1
-2 0 1
Output
3
Input
1 2
-1 0 1 0
-100 0 1
100 0 1
Output
0
Note

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