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문제

린셰핑(Linköping)의 수도 시설은 복잡하다. 린셰핑 근교에는 지하수를 뽑는 수원지가 몇개 있다. 지하수는 파이프를 통해서 전달되는데, 파이프는 직선으로 한 수원지와 한 도시의 지점을 잇는다.

파이프의 지하 깊이는 모두 같아서. 두 파이프가 교차하면 교차점을 만든다. 교차점에서는 정확히 두개의 파이프만이 만남을 보장한다. 수원지는 교차점으로 치지 않으며, 수원지에서는 0개 이상의 파이프가 출발할 수 있다.

교차점에는 가끔 이물질이 막히는데, 이러한 이물질은 파이프에 큰 부담을 주어서 싱크홀 현상을 만든다. 최근 캠릿브지 대학의 연구에 의하면, 이러한 싱크홀을 본 린셰핑의 대학생들은 보통 인생의 회의를 느끼고, 공부를 그만두며, 결국 사회의 붕괴를 초래한다고 한다. 사회의 유지를 위해서, 린셰핑의 수도 시설 관리 기업인 Nordic Water Extraction and Redistribution Company (NWERC) 는 로봇을 설계했다. 로봇은 수원지에서 파이프로 집어넣을 수 있으며, 파이프를 한번 왔다갔다하면서 파이프에 있는 모든 교차점을 청소한다. 정부에서는, 교차점에서 로봇이 충돌하는 일을 막기 위해, 두 파이프가 만나는 교차점이 있다면, 오직 한 파이프만이 로봇을 포함할 수 있다는 규정을 만들었다.

파이프를 청소하는 동안에는 수도 시설이 닫힌다 (이것도 정부 규정이다). 고로, NWERC는 한번의 로봇 청소만으로 모든 파이프를 청소하고자 한다. 당신은, 어떠한 파이프의 부분집합에 동시에 로봇을 삽입해서, 로봇들이 모든 교차점을 청소하고, 두 로봇이 충돌하는 일이 없는지를 판별하여야 한다.

입력

입력은 다음과 같다.

  • 첫 번째 줄에는 w (1 ≤ w ≤ 1,000), p(1 ≤ p ≤ 1,000) 가 주어진다. w는 수원지의 개수, p는 파이프의 개수를 뜻한다.
  • 이후 w개의 줄에 xi and yi (−10 000 ≤ x, y ≤ 10 000) 가 주어진다. i번 수원지의 위치를 뜻한다. (수원지는 1부터 w까지 순서대로 번호가 붙어있다)
  • 이후 p개의 줄에 세 정수 s (1 ≤ s ≤ w), x, y (−10 000 ≤ x, y ≤ 10 000) 가 주어진다. 파이프가 s번 수원지에서 출발해서 (x, y)에서 종료함을 뜻한다.

각각의 파이프는 1개의 수원지(=시작점) 만을 포함하며, 3개 이상의 파이프가 만나는 모든 점은 수원지다. 두 파이프는 많아야 1개의 교점을 가지며, 교점은 파이프의 끝점에 있을 수도 있다. 모든 파이프의 길이는 0 초과이다.

출력

판별 결과에 따라 가능하면 "possible", 아니면 "impossible"을 출력한다.

예제 입력 1

3 3
0 0
0 2
2 0
1 2 3
2 2 2
3 0 3

예제 출력 1

impossible

예제 입력 2

2 3
0 0
0 10
1 5 15
1 2 15
2 10 10

예제 출력 2

possible
[{"problem_id":"11668","problem_lang":"0","title":"\ud30c\uc774\ud504 \uccad\uc18c","description":"<p>\ub9b0\uc170\ud551(Link&ouml;ping)\uc758 \uc218\ub3c4 \uc2dc\uc124\uc740 \ubcf5\uc7a1\ud558\ub2e4. \ub9b0\uc170\ud551 \uadfc\uad50\uc5d0\ub294 \uc9c0\ud558\uc218\ub97c \ubf51\ub294 \uc218\uc6d0\uc9c0\uac00 \uba87\uac1c \uc788\ub2e4. \uc9c0\ud558\uc218\ub294 \ud30c\uc774\ud504\ub97c \ud1b5\ud574\uc11c \uc804\ub2ec\ub418\ub294\ub370, \ud30c\uc774\ud504\ub294 \uc9c1\uc120\uc73c\ub85c \ud55c \uc218\uc6d0\uc9c0\uc640 \ud55c \ub3c4\uc2dc\uc758 \uc9c0\uc810\uc744 \uc787\ub294\ub2e4.<\/p>\r\n\r\n<p>\ud30c\uc774\ud504\uc758 \uc9c0\ud558 \uae4a\uc774\ub294 \ubaa8\ub450 \uac19\uc544\uc11c. \ub450 \ud30c\uc774\ud504\uac00 \uad50\ucc28\ud558\uba74 \uad50\ucc28\uc810\uc744 \ub9cc\ub4e0\ub2e4. \uad50\ucc28\uc810\uc5d0\uc11c\ub294 \uc815\ud655\ud788 \ub450\uac1c\uc758 \ud30c\uc774\ud504\ub9cc\uc774 \ub9cc\ub0a8\uc744 \ubcf4\uc7a5\ud55c\ub2e4. \uc218\uc6d0\uc9c0\ub294 \uad50\ucc28\uc810\uc73c\ub85c \uce58\uc9c0 \uc54a\uc73c\uba70, \uc218\uc6d0\uc9c0\uc5d0\uc11c\ub294 0\uac1c \uc774\uc0c1\uc758 \ud30c\uc774\ud504\uac00 \ucd9c\ubc1c\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uad50\ucc28\uc810\uc5d0\ub294 \uac00\ub054 \uc774\ubb3c\uc9c8\uc774 \ub9c9\ud788\ub294\ub370, \uc774\ub7ec\ud55c \uc774\ubb3c\uc9c8\uc740 \ud30c\uc774\ud504\uc5d0 \ud070 \ubd80\ub2f4\uc744 \uc8fc\uc5b4\uc11c \uc2f1\ud06c\ud640 \ud604\uc0c1\uc744 \ub9cc\ub4e0\ub2e4. \ucd5c\uadfc \ucea0\ub9bf\ube0c\uc9c0 \ub300\ud559\uc758 \uc5f0\uad6c\uc5d0 \uc758\ud558\uba74, \uc774\ub7ec\ud55c \uc2f1\ud06c\ud640\uc744 \ubcf8 \ub9b0\uc170\ud551\uc758 \ub300\ud559\uc0dd\ub4e4\uc740 \ubcf4\ud1b5 \uc778\uc0dd\uc758 \ud68c\uc758\ub97c \ub290\ub07c\uace0, \uacf5\ubd80\ub97c \uadf8\ub9cc\ub450\uba70, \uacb0\uad6d \uc0ac\ud68c\uc758 \ubd95\uad34\ub97c \ucd08\ub798\ud55c\ub2e4\uace0 \ud55c\ub2e4.&nbsp;\uc0ac\ud68c\uc758 \uc720\uc9c0\ub97c \uc704\ud574\uc11c, \ub9b0\uc170\ud551\uc758 \uc218\ub3c4 \uc2dc\uc124 \uad00\ub9ac \uae30\uc5c5\uc778 Nordic Water Extraction and Redistribution Company (NWERC) \ub294 \ub85c\ubd07\uc744 \uc124\uacc4\ud588\ub2e4. \ub85c\ubd07\uc740 \uc218\uc6d0\uc9c0\uc5d0\uc11c \ud30c\uc774\ud504\ub85c \uc9d1\uc5b4\ub123\uc744 \uc218 \uc788\uc73c\uba70, \ud30c\uc774\ud504\ub97c \ud55c\ubc88 \uc654\ub2e4\uac14\ub2e4\ud558\uba74\uc11c \ud30c\uc774\ud504\uc5d0 \uc788\ub294 \ubaa8\ub4e0 \uad50\ucc28\uc810\uc744 \uccad\uc18c\ud55c\ub2e4. \uc815\ubd80\uc5d0\uc11c\ub294, \uad50\ucc28\uc810\uc5d0\uc11c \ub85c\ubd07\uc774 \ucda9\ub3cc\ud558\ub294 \uc77c\uc744 \ub9c9\uae30 \uc704\ud574, \ub450 \ud30c\uc774\ud504\uac00 \ub9cc\ub098\ub294 \uad50\ucc28\uc810\uc774 \uc788\ub2e4\uba74, \uc624\uc9c1 \ud55c \ud30c\uc774\ud504\ub9cc\uc774 \ub85c\ubd07\uc744 \ud3ec\ud568\ud560 \uc218 \uc788\ub2e4\ub294 \uaddc\uc815\uc744 \ub9cc\ub4e4\uc5c8\ub2e4.<\/p>\r\n\r\n<p>\ud30c\uc774\ud504\ub97c \uccad\uc18c\ud558\ub294 \ub3d9\uc548\uc5d0\ub294 \uc218\ub3c4 \uc2dc\uc124\uc774 \ub2eb\ud78c\ub2e4 (\uc774\uac83\ub3c4 \uc815\ubd80 \uaddc\uc815\uc774\ub2e4). \uace0\ub85c, NWERC\ub294 \ud55c\ubc88\uc758 \ub85c\ubd07 \uccad\uc18c\ub9cc\uc73c\ub85c \ubaa8\ub4e0 \ud30c\uc774\ud504\ub97c \uccad\uc18c\ud558\uace0\uc790 \ud55c\ub2e4. \ub2f9\uc2e0\uc740, \uc5b4\ub5a0\ud55c \ud30c\uc774\ud504\uc758 \ubd80\ubd84\uc9d1\ud569\uc5d0 \ub3d9\uc2dc\uc5d0 \ub85c\ubd07\uc744 \uc0bd\uc785\ud574\uc11c, \ub85c\ubd07\ub4e4\uc774 \ubaa8\ub4e0 \uad50\ucc28\uc810\uc744 \uccad\uc18c\ud558\uace0, \ub450 \ub85c\ubd07\uc774 \ucda9\ub3cc\ud558\ub294 \uc77c\uc774 \uc5c6\ub294\uc9c0\ub97c \ud310\ubcc4\ud558\uc5ec\uc57c \ud55c\ub2e4.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uccab \ubc88\uc9f8 \uc904\uc5d0\ub294 w (1 &le; w &le; 1,000), p(1 &le; p &le; 1,000) \uac00 \uc8fc\uc5b4\uc9c4\ub2e4. w\ub294 \uc218\uc6d0\uc9c0\uc758 \uac1c\uc218, p\ub294 \ud30c\uc774\ud504\uc758 \uac1c\uc218\ub97c \ub73b\ud55c\ub2e4.<\/li>\r\n\t<li>\uc774\ud6c4 w\uac1c\uc758 \uc904\uc5d0 x<sub>i<\/sub> and y<sub>i<\/sub> (&minus;10 000 &le; x, y &le; 10 000) \uac00 \uc8fc\uc5b4\uc9c4\ub2e4. i\ubc88 \uc218\uc6d0\uc9c0\uc758 \uc704\uce58\ub97c \ub73b\ud55c\ub2e4. (\uc218\uc6d0\uc9c0\ub294 1\ubd80\ud130 w\uae4c\uc9c0 \uc21c\uc11c\ub300\ub85c \ubc88\ud638\uac00 \ubd99\uc5b4\uc788\ub2e4)<\/li>\r\n\t<li>\uc774\ud6c4 p\uac1c\uc758 \uc904\uc5d0 \uc138 \uc815\uc218 s (1 &le; s &le; w), x, y (&minus;10 000 &le; x, y &le; 10 000) \uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ud30c\uc774\ud504\uac00 s\ubc88 \uc218\uc6d0\uc9c0\uc5d0\uc11c \ucd9c\ubc1c\ud574\uc11c (x, y)\uc5d0\uc11c \uc885\ub8cc\ud568\uc744 \ub73b\ud55c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uac01\uac01\uc758 \ud30c\uc774\ud504\ub294 1\uac1c\uc758 \uc218\uc6d0\uc9c0(=\uc2dc\uc791\uc810) \ub9cc\uc744 \ud3ec\ud568\ud558\uba70, 3\uac1c \uc774\uc0c1\uc758 \ud30c\uc774\ud504\uac00 \ub9cc\ub098\ub294 \ubaa8\ub4e0 \uc810\uc740 \uc218\uc6d0\uc9c0\ub2e4. \ub450 \ud30c\uc774\ud504\ub294 \ub9ce\uc544\uc57c 1\uac1c\uc758 \uad50\uc810\uc744 \uac00\uc9c0\uba70, \uad50\uc810\uc740 \ud30c\uc774\ud504\uc758 \ub05d\uc810\uc5d0 \uc788\uc744 \uc218\ub3c4 \uc788\ub2e4. \ubaa8\ub4e0 \ud30c\uc774\ud504\uc758 \uae38\uc774\ub294 0 \ucd08\uacfc\uc774\ub2e4.<\/p>\r\n","output":"<p>\ud310\ubcc4 \uacb0\uacfc\uc5d0 \ub530\ub77c \uac00\ub2a5\ud558\uba74 &quot;possible&quot;, \uc544\ub2c8\uba74 &quot;impossible&quot;\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"11668","problem_lang":"1","title":"Cleaning Pipes","description":"<p>Link&ouml;ping has a quite complex water transport system. Around Link&ouml;ping there are several wells from which water is drawn. The water is then transported to other locations using pipes. Each pipe is a straight canal from one of the wells to some location in the city.<\/p>\r\n\r\n<p>All the pipes are at the same depth under ground. Therefore, whenever two pipes cross, they form an intersection. Luckily the pipe system was constructed in such a way that exactly two pipes meet at each such intersection. The wells do not count as intersections. Any number of pipes (including zero or more than two) may originate at each well.<\/p>\r\n\r\n<p>The intersections pose a problem, since dirt (a mixture of lime and other &ldquo;remains&rdquo;) tends to get stuck there. This dirt causes the pipes to degrade and collapse, leading to the formation of large sink holes. Such sink holes have a mesmerising effect on the students in Link&ouml;ping, causing them to neglect their studies and remain uneducated, which in the long run will lead to a collapse of not just the pipe system but of the very fabric of society. Therefore it is imperative that the pipes are regularly cleaned. The Nordic Water Extraction and Redistribution Company (NWERC) &ndash; which is in charge of Link&ouml;ping&rsquo;s waterpipes &ndash; has an ample fleet of robots to perform this task. A robot can be inserted into a pipe at the well where the pipe begins. The robot then goes through the pipe all the way to its end and cleans all intersections along the way. After reaching the end, the robot turns around and returns back to the well where it started. In order to prevent robot collisions, government regulations stipulate that whenever two pipes intersect, at most one of them may contain a robot.<\/p>\r\n\r\n<p>Since the whole water system has to be shut down while it is being cleaned (another government regulation), the NWERC would like to do the cleaning quickly, by using a single batch of cleaning robots, all started at the same time.<\/p>\r\n\r\n<p>Your task is to verify whether this can be done &ndash; i.e., whether we can simultaneously insert robots into a subset of the pipes in such a way that the robots will clean all intersections and there will be no risk of two robots colliding.<\/p>\r\n","input":"<p>The input consists of:<\/p>\r\n\r\n<ul>\r\n\t<li>one line with two integers w (1 &le; w &le; 1 000), the number of wells, and p (1 &le; p &le; 1 000), the number of pipes;<\/li>\r\n\t<li>w lines, the ith of which contains two integers x<sub>i<\/sub> and y<sub>i<\/sub> (&minus;10 000 &le; x, y &le; 10 000), the position of well number i (the wells are numbered from 1 to w);<\/li>\r\n\t<li>p lines each with three integers s (1 &le; s &le; w), the well at which the pipe starts, and x and y (&minus;10 000 &le; x, y &le; 10 000), the position at which the pipe ends.<\/li>\r\n<\/ul>\r\n\r\n<p>Each pipe will contain exactly one well, the one at which it starts. Any point shared by more than two pipes will be a well. Any two pipes share at most one common point. The common point of two pipes may be the endpoint of one or both of them. All pipes have positive length.<\/p>\r\n","output":"<p>If it is possible to clean all intersections as described above, output &ldquo;possible&rdquo;. Otherwise, output &ldquo;impossible&rdquo;.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

ICPC > Regionals > Europe > Northwestern European Regional Contest > NWERC 2015 C번

  • 문제를 번역한 사람: koosaga
  • 데이터를 추가한 사람: mym0404
  • 문제를 만든 사람: Gregor Behnke