The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

Codeforces Round 203 (Div. 2) |
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Finished |

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D. Looking for Owls

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputEmperor 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:

- circles
*i*and*j*are symmetrical relatively to the straight line containing segment*k*; - circles
*i*and*j*don't have any common points; - circles
*i*and*j*have the same radius; - 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* ≤ 3·10^{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.

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.

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