O. Circular Mazetime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given a circular maze such as the ones shown in the figures.    Determine if it can be solved, i.e., if there is a path which goes from the center to the outside of the maze which does not touch any wall. The maze is described by n walls. Each wall can be either circular or straight.   Circular walls are described by a radius r, the distance from the center, and two angles \theta_1, \theta_2 describing the beginning and the end of the wall in the clockwise direction. Notice that swapping the two angles changes the wall.  Straight walls are described by an angle \theta, the direction of the wall, and two radii r_1 < r_2 describing the beginning and the end of the wall. Angles are measured in degrees; the angle 0 corresponds to the upward pointing direction; and angles increase clockwise (hence the east direction corresponds to the angle 90).InputEach test contains multiple test cases. The first line contains an integer t (1\le t\le 20) — the number of test cases. The descriptions of the t test cases follow.The first line of each test case contains an integer n (1 \leq n \leq 5000) — the number of walls. Each of the following n lines each contains a character (C for circular, and S for straight) and three integers:   either r, \theta_1, \theta_2 (1 \leq r \leq 20 and 0 \leq \theta_1,\theta_2 < 360 with \theta_1 \neq \theta_2) if the wall is circular,  or r_1, r_2 and \theta (1 \leq r_1 < r_2 \leq 20 and 0 \leq \theta < 360) if the wall is straight. It is guaranteed that circular walls do not overlap (but two circular walls may intersect at one or two points), and that straight walls do not overlap (but two straight walls may intersect at one point). However, circular and straight walls can intersect arbitrarily.OutputFor each test case, print YES if the maze can be solved and NO otherwise. ExampleInput
2
5
C 1 180 90
C 5 250 230
C 10 150 140
C 20 185 180
S 1 20 180
6
C 1 180 90
C 5 250 230
C 10 150 140
C 20 185 180
S 1 20 180
S 5 10 0
Output
YES
NO
NoteThe two sample test cases correspond to the two mazes in the picture.
2
5
C 1 180 90
C 5 250 230
C 10 150 140
C 20 185 180
S 1 20 180
6
C 1 180 90
C 5 250 230
C 10 150 140
C 20 185 180
S 1 20 180
S 5 10 0

YES NO 
['brute force', 'dfs and similar', 'graphs', 'implementation']