A Cut Rectangle

Input

First, two positive numbers, $X$ and $Y$, are provided, representing the coordinates of the top right corner of the rectangle. The rectangle is positioned in a coordinate system such that its bottom left corner is at coordinates $0,0$, with its sides parallel to the coordinate axes.

Next, an integer $N$ is given, indicating the number of cuts (1 \leq N \leq 200). Each cut is described by a straight line. Each line is defined by three numbers $A$, $B$, and $C$, such that all points $(x,y)$ on this line satisfy the equation A x + B y + C = 0 (where A^2 + B^2 > 0 is always true).

All numbers entered (except $N$) are real, given with two decimal places, and do not exceed 10^4. No two lines coincide, and none of them align with the sides of the rectangle. Each cut passes through points inside the given rectangle.

Output

Output a single integer, which is the number of sections of the rectangle that are triangular.

Examples