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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.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

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