Problem Description

Planet X is very special: its rotation speed is the same as its revolution speed, so sunlight always shines at a fixed angle.

Recently, to develop interstellar tourism, Planet X rents out positions in space to tourists from Country Y for sunbathing. Each rented spot is a disk-shaped colored cloud floating in the air (the disk is parallel to the ground). Of course, this will block part of the sunlight, and plants on the blocked land cannot grow.

The task of this problem is to compute how large the area of land on a certain farm is that is suitable for growing crops.

Input Format

The first line of the input contains two integers $a,b$, representing the length and width of a farm as $a$ and $b$. The farm area is the rectangular region enclosed by the coordinates $(0,0,0),(a,0,0),(a,b,0),(0,b,0)$.

The second line contains a real number $g$, representing the angle of sunlight. For simplicity, we assume the sunlight rays are perpendicular to the farm’s width, and the angle between them and the farm’s length is $g$ degrees. Then, the projection of a point $(x,y,z)$ in space onto the ground should be $(x+z \times \ctg(g),y,0)$, where $\ctg(g)$ denotes the cotangent value corresponding to $g$ degrees.

The third line contains a non-negative integer $n$, representing the number of rented spots in the air.

The next $n$ lines describe each rented spot. The $i$-th line contains $4$ integers $x_i,y_i,z_i,r_i$, indicating that the center of the $i$-th colored cloud is at $(x_i,y_i,z_i)$ and its radius is $r_i$.

Output Format

Output a real number, rounded to two decimal places, representing the area of land on the farm where crops can grow.

10 10
90.0
1
5 5 10 5

21.46

8 8
90.0
1
4 4 10 5

1.81

20 10
45.0
2
5 0 5 5
8 6 14 6

130.15

Hint

Time limit: 1 second, 64M. The 4th Lanqiao Cup National Contest in 2013.

Translated by ChatGPT 5