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문제

악마 박승원은 세계에서 가장 강력한 레이저를 찾기 위해 당신을 찾았다. 당신은 레이저 프로토타입이 있지만, 박승원에게 레이저 제작 예산을 받기 위해서는 시뮬레이션을 박승원에게 보여주어야 한다.

시뮬레이션은 2차원 평면 상에서 "거울", "광선 스플리터", "광선 감지기" 를 둠으로써 시작된다. 각 물체들은 선분으로 모델링된다.

  • 거울 : 거울에 닿는 광선은 반대 방향으로 나아간다.
  • 감지기 : 감지기는 들어오는 광선을 흡수한다.
  • 스플리터 : 스플리터는 들어오는 광선을 두 광선으로 나눈다 - 한 광선은 스플리터를 관통하는 방향, 나머지 광선은 스플리터에 반사되는 방향이다.

시작점과 방향이 주어진 레이저가 발사되었을 때. 당신은 어떠한 감지기가 광선을 흡수했는지를 구해야 한다. 문제를 쉽게 하기 위해 다음과 같은 가정이 가능하다.

  • 100 * 100 크기의 사각형 구역만 시뮬레이션하면 되며, 모든 물체는 해당 구역 안에 존재한다.
  • 주어지는 선분들이 겹치거나 교점을 갖는 일은 없다.
  • 사각형 구역의 가장자리에서 레이저는 발사된다.
  • 시뮬레이션은 모든 광선이 테이블을 빠져나오거나 감지기에 흡수당했을 때 종료된다.
  • 레이저 광선은 시뮬레이션을 통틀어 100번 이상 반사되지 않는다.
  • 감지기는 1개 이상 존재한다.
  • 시뮬레이션 과정에서 레이저 광선이 어떠한 물체와 한 직선 상에 놓여있는 일은 없다.

입력

첫 번째 줄에는 테스트 데이터의 수 N이 주어진다. 주어지는 데이터들은 다음과 같다 -

  • 첫 번째 줄에는 "x,y i,j" 꼴로 테이블의 가장자리 중 하나인 시작점 (x,y) 와, 레이저 광선의 방향벡터 (i,j) 가 주어진다. (−1024 ≤ i,j ≤ 1024) 주어지는 수는 모두 정수이다.
  • 두 번째 줄에는 물체의 수 P가 주어진다. (1 ≤ P ≤ 100)
  • 이후 P개의 줄에 각각 물체들이 주어진다. "M"은 거울, "S"는 스플리터, "D"는 감지기를 뜻하며, 물체가 점유하는 각 끝점 두개가 "x,y" 꼴로 주어진다.

출력

각각의 테스트 케이스에 대해 먼저 첫 줄에 "DATA SET #k"를 출력하라. k는 테스트 케이스의 번호다.

만약 레이저 빔을 흡수한 감지기가 없다면, "NO BEAMS DETECTED"를 출력한다.

이외의 경우 레이저를 흡수한 감지기의 번호를 오름차순으로 출력하라.

예제 입력 1

1
50,100 0,-1
6
D 0,40 20,20
M 40,20 60,40
D 80,20 100,40
D 0,70 20,90
S 40,90 60,70
D 80,90 100,70

예제 출력 1

DATA SET #1
1
6

힌트

Enigma - The Screen Behind The Mirror

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(&minus;1024 &le; i,j &le; 1024) \uc8fc\uc5b4\uc9c0\ub294 \uc218\ub294 \ubaa8\ub450 \uc815\uc218\uc774\ub2e4.<\/li>\r\n\t<li>\ub450 \ubc88\uc9f8 \uc904\uc5d0\ub294 \ubb3c\uccb4\uc758 \uc218 P\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; P &le; 100)<\/li>\r\n\t<li>\uc774\ud6c4 P\uac1c\uc758 \uc904\uc5d0 \uac01\uac01 \ubb3c\uccb4\ub4e4\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. &quot;M&quot;\uc740 \uac70\uc6b8, &quot;S&quot;\ub294 \uc2a4\ud50c\ub9ac\ud130, &quot;D&quot;\ub294 \uac10\uc9c0\uae30\ub97c \ub73b\ud558\uba70, \ubb3c\uccb4\uac00 \uc810\uc720\ud558\ub294 \uac01 \ub05d\uc810 \ub450\uac1c\uac00 &quot;x,y&quot; \uaf34\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/li>\r\n<\/ul>\r\n","output":"<p>\uac01\uac01\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574 \uba3c\uc800 \uccab \uc904\uc5d0 &quot;DATA SET #k&quot;\ub97c \ucd9c\ub825\ud558\ub77c. k\ub294 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \ubc88\ud638\ub2e4.<\/p>\r\n\r\n<p>\ub9cc\uc57d \ub808\uc774\uc800 \ube54\uc744 \ud761\uc218\ud55c \uac10\uc9c0\uae30\uac00 \uc5c6\ub2e4\uba74, &quot;NO BEAMS DETECTED&quot;\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc774\uc678\uc758 \uacbd\uc6b0 \ub808\uc774\uc800\ub97c \ud761\uc218\ud55c \uac10\uc9c0\uae30\uc758 \ubc88\ud638\ub97c \uc624\ub984\ucc28\uc21c\uc73c\ub85c \ucd9c\ub825\ud558\ub77c.<\/p>\r\n","hint":"<p>Enigma - The Screen Behind The Mirror<\/p>\r\n\r\n<p><iframe frameborder=\"0\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/ZcxJE_TOGJY\" width=\"560\"><\/iframe><\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"4532","problem_lang":"1","title":"The Screen Behind the Mirror","description":"<p>Dr. Evil has contracted your valuable services to build for him the world&#39;s most powerful &quot;laser&quot;. Of course before you spend one billion dollars building the thing, you want to run some simulations first to make sure everything will work as designed. For this phase of the project, you will be simulating part of the aiming system which uses mirrors and other optics to change the direction of the laser beam.<\/p>\r\n\r\n<p>The simulation consists of a flat square table with mirrors, beam splitters, and beam detectors arranged on the tabletop, and with each object represented by a one dimensional line segment. The list below describes each of the object types in detail:<\/p>\r\n\r\n<ul>\r\n\t<li>mirror : A mirror object will reflect any laser beam striking its surface. The reflected beam leaves at the same angle of incidence as the incoming beam. Note that both sides of a mirror object are reflective.<\/li>\r\n\t<li>detector : A detector is an opaque object which absorbs any laser beam striking it. The simulation must also keep track of which detectors are struck by a laser for program output purposes. Note that a laser beam strike on either side of a detector counts as a &quot;hit&quot;.<\/li>\r\n\t<li>splitter : When a laser beam strikes a splitter, it divides into two beams. One of the new beams will reflect from the splitter surface (as with a mirror), and the other beam will pass through the splitter without changing direction. A splitter will function the same way regardless which side of it is struck by a laser beam.<\/li>\r\n<\/ul>\r\n\r\n<p>See the figures below for examples of a laser beam&#39;s interaction with each of the possible object types:<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"\/upload\/images2\/mirror.png\" style=\"height:202px; width:444px\" \/><\/p>\r\n\r\n<p>For each simulation, a single laser beam enters the tabletop area. The program must compute the path taken by the laser beam (including secondary beams due to splitters), and it must determine which detectors are struck by a laser beam.<\/p>\r\n\r\n<p>You can make the following assumptions in the program:<\/p>\r\n\r\n<ol>\r\n\t<li>The tabletop surface is a 100 by 100 square, and unless otherwise specified all coordinates in the program&#39;s input are given as integers within the tabletop area (i.e. between 0 and 100 inclusive).<\/li>\r\n\t<li>There will be no overlaps between the line segment objects.<\/li>\r\n\t<li>The laser which enters the tabletop area always starts from the edge of the table.<\/li>\r\n\t<li>The simulation of each data set ends when all laser beams have either exited the table top area or have terminated at a detector.<\/li>\r\n\t<li>For each data set there will be no more than 100 total reflections among all laser beams in that data set.<\/li>\r\n\t<li>A laser beam will never intersect any object on a vertex and will never be collinear with an object&#39;s line segment.<\/li>\r\n\t<li>Each data set will contain at least one detector object.<\/li>\r\n<\/ol>\r\n","input":"<p>Input to this problem will begin with a line containing a single integer N (1 &le; N &le; 100) indicating the number of data sets. Each data set consists of the following components:<\/p>\r\n\r\n<ul>\r\n\t<li>A single line with four numbers &quot;x,y i,j&quot; where x,y is a point along the table edge at which the laser beam enters, and i,j is a vector with integer components (&minus;1024 &le; i,j &le; 1024) specifying the direction of the incoming laser beam, where i corresponds to the x-axis direction and j corresponds to the y-axis direction.<\/li>\r\n\t<li>A line with a single integer P (1 &le; P &le; 100) giving the total number of objects in this data set.<\/li>\r\n\t<li>A series of P lines, each representing one object, with the first line describing object 1, the second line describing object 2, and so on. Each line begins with a single letter specifying the object type where a &quot;M&quot; indicates a mirror object, &quot;S&quot; a splitter, and &quot;D&quot; a detector. This is followed by two coordinate pairs of the form &quot;x,y&quot;, specifying the two end points of the object&#39;s line segment.<\/li>\r\n<\/ul>\r\n","output":"<p>For each data set in the input, output the heading &quot;DATA SET #k&quot; where k is 1 for the first data set, 2 for the second, etc. If in this data set none of the detector objects are struck by any laser beams, output the message &quot;NO BEAMS DETECTED&quot;. Otherwise, output the object number, one per line, of each detector struck by a laser beam. The list of detectors should be sorted by their object numbers and output in ascending order. If a detector is struck by more than one laser beam, it should only be listed once in the output.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]