Problem B

Bisectors
Input: Standard Input

Output: Standard Output

We all probably know how to find equation of bisectors in Coordinate Geometry. If the equations of two lines are and , then the equations of the bisectors of the four angles they create are given by. Now one has to be quite intelligent to find out for which angles to choose the ‘+’(plus) sign and for which angles to choose the ‘-’(minus) sign. You will have to do similar sort of choosing in this problem. Suppose there is a fixed point (C_x, C_y) and there are n (n≤10000) other points around it. No two points from these n points are collinear with (C_x, C_y). If you connect all these point with (C_x, C_y) you will get a star-topology like image made of n lines. The equations of these n lines are also given and only these equations must be used when finding the equation of bisectors. This n lines create n(n-1)/2 acute or obtuse angles in total and so they have total n(n-1)/2 bisectors. You have to find out how many of these bisectors have equations formed using the + sign. The image below shows an image where n=5, C_x=5 and C_y=2. This image corresponds to the only sample input.

Figure: Five lines above create 5(5-1)/2=10 angles and these angles has 10 bisectors. Of these 10 bisectors, the equation of only 4 are formed using the + sign of the formula

Input

The input file contains maximum 35 sets of inputs. The description of each set is given below:

First line of each set contains three integers C_x, C_y (-10000 ≤ C_x, C_y ≤ 10000) and n (0 ≤ n ≤
10000). Each of the next n lines contains two integers xi, yi (20000 ≤ xi, yi ≤ 20000) and a string of the form a_ix+b_iy+c_i=0. Here (xi, yi) is the coordinate of a point around (Cx, Cy) and the string denotes the equation of the line segment formed by connecting (C_x, C_y) and (xi, yi). You can assume that (-100000 ≤ a_i, b_i ≤ 100000) and (-2000000000 ≤ c_i ≤ 2000000000). This equation will actually be used to find the equations of bisectors of the angles that this line creates.

Input is terminated by a set where the value of n is zero.

Output

For each set of input produce one line of output. This line contains an integer number P that denotes of the bisector equations how many are formed using the + sign in the bisector equation .

Sample Input	Output for Sample Input
5 2 5 12 7 10x-14y-22=0 1 -4 24x-16y-88=0 4 10 32x+4y-168=0 -1 9 56x+48y-376=0 12 -3 -10x-14y+78=0 10 10 0	4

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Problemsetter: Shahriar Manzoor

Special Thanks: Derek Kisman