Hitting the Targets
A fundamental operation in computational geometry is determining whether two objects touch. For example, in a game that involves shooting, we want to determine if a player’s shot hits a target. A shot is a two dimensional point, and a target is a two dimensional enclosed area. A shot hits a target if it is inside the target. The boundary of a target is inside the target. Since it is possible for targets to overlap, we want to identify how many targets a shot hits.
The figure above illustrates the targets (large unfilled rectangles and circles) and shots (filled circles) of the sample input. The origin $(0, 0)$ is indicated by a small unfilled circle near the center.
Input starts with an integer $1 \leq m \leq 30$ indicating the number of targets. Each of the next $m$ lines begins with the word rectangle or circle and then a description of the target boundary. A rectangular target’s boundary is given as four integers $x_1~ y_1~ x_2~ y_2$, where $x_1<x_2$ and $y_1<y_2$. The points $(x_1,y_1)$ and $(x_2,y_2)$ are the bottom-left and top-right corners of the rectangle, respectively. A circular target’s boundary is given as three integers $x~ y~ r$. The center of the circle is at $(x,y)$ and the $0<r\leq 1\, 000$ is the radius of the circle.
After the target descriptions is an integer $1 \leq n \leq 100$ indicating the number of shots that follow. The next $n$ lines each contain two integers $x~ y$, indicating the coordinates of a shot. All $x$ and $y$ coordinates for targets and shots are in the range $[-1\, 000,1\, 000]$.
For each of the $n$ shots, print the total number of targets the shot hits.
|Sample Input 1||Sample Output 1|
3 rectangle 1 1 10 5 circle 5 0 8 rectangle -5 3 5 8 5 1 1 4 5 10 10 -10 -1 4 -3
2 3 0 0 1