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문제

주식회사 금고는 매우 안전한 금고를 만드는 회사이다. 금고사의 최신 금고는 빛을 이용한다. 직사각형 그리드에 거울을 적절히 넣고, 레이저를 발사해 감지기에 레이저가 감지되는지를 확인한다.

레이저는 그리드의 가장 윗 행의 왼쪽에서 발사된다. 레이저가 거울을 만난 경우에 레이저는 반사된다. 모든 거울은 45도 대각선 방향 (\ 또는 /)이다. 레이저가 가장 아랫 행의 오른쪽으로 빠져 나올 때(왼쪽 그림), 금고가 열린다. 그 외의 경우에는 알람이 울린다.

모든 금고에는 거울이 한 개씩 빠져있다. (오른쪽 그림) 사용자는 거울 한 개를 비어있는 칸에 넣는다. 올바른 사용자는 거울의 정확한 위치와 모양 (4행 3열, /)을 알고 있기 때문에, 금고를 안전하게 열 수 있다.

금고의 정보가 주어졌을 때, 금고가 안전한지 아닌지 구하는 프로그램을 작성하시오. 안전한 금고는 거울을 넣지 않았을 때 열리면 안되며, 금고를 열 수 있는 거울의 위치와 모양이 적어도 한 개는 존재한다.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있고 각 테스트 케이스는 금고 하나를 나타낸다.

테스트 케이스의 첫째 줄에는 네정수 r, c, m, n이 주어진다. (1 ≤ r,c ≤ 1,000,000, 0 ≤ m,n ≤ 200,000) 금고는 r행 c열로 이루어져 있다.

다음 m개 줄에는 두 정수 ri와 ci (1 ≤ ri ≤ r, 1 ≤ ci ≤ c)가 주어지며, ri행 ci 열에 /모양의 거울이 있다는 뜻이다.

다음 n개 줄에도 \모양 거울의 정보가 주어지며, /모양 정보와 같은 방식으로 주어진다.

모든 m+n개의 위치는 서로 다르다. 

출력

각 테스트 케이스마다, 테스트 케이스 번호를 출력하고 다음을 출력한다.

  • 0 거울을 삽입하지 않고 금고를 열 수 있을때
  • k r c 거울을 넣지 않으면 금고가 열리지 않고, 금고를 열 수 있는 위치의 수가 k개, 그 중 가장 사전순으로 앞서는 위치가 (r, c)인 경우 (한 위치에 /와 \ 모양의 거울을 넣을 수 있는 경우에 위치 1개로 센다)
  • impossible 거울을 넣어도 금고를 열 수 없는 경우

예제 입력 1

5 6 1 4
2 3
1 2
2 5
4 2
5 5
100 100 0 2
1 77
100 77
100 100 0 0

예제 출력 1

Case 1: 2 4 3
Case 2: 0
Case 3: impossible
[{"problem_id":"4211","problem_lang":"0","title":"\uae08\uace0 \ud68c\uc0ac","description":"<p>\uc8fc\uc2dd\ud68c\uc0ac \uae08\uace0\ub294 \ub9e4\uc6b0 \uc548\uc804\ud55c \uae08\uace0\ub97c \ub9cc\ub4dc\ub294 \ud68c\uc0ac\uc774\ub2e4. \uae08\uace0\uc0ac\uc758 \ucd5c\uc2e0 \uae08\uace0\ub294 \ube5b\uc744 \uc774\uc6a9\ud55c\ub2e4. \uc9c1\uc0ac\uac01\ud615 \uadf8\ub9ac\ub4dc\uc5d0 \uac70\uc6b8\uc744 \uc801\uc808\ud788 \ub123\uace0, \ub808\uc774\uc800\ub97c \ubc1c\uc0ac\ud574 \uac10\uc9c0\uae30\uc5d0 \ub808\uc774\uc800\uac00 \uac10\uc9c0\ub418\ub294\uc9c0\ub97c \ud655\uc778\ud55c\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/mirro.png\" style=\"height:178px; width:600px\" \/><\/p>\r\n\r\n<p>\ub808\uc774\uc800\ub294 \uadf8\ub9ac\ub4dc\uc758 \uac00\uc7a5 \uc717 \ud589\uc758 \uc67c\ucabd\uc5d0\uc11c \ubc1c\uc0ac\ub41c\ub2e4. \ub808\uc774\uc800\uac00 \uac70\uc6b8\uc744 \ub9cc\ub09c \uacbd\uc6b0\uc5d0 \ub808\uc774\uc800\ub294 \ubc18\uc0ac\ub41c\ub2e4. \ubaa8\ub4e0 \uac70\uc6b8\uc740 45\ub3c4 \ub300\uac01\uc120 \ubc29\ud5a5 (\\ \ub610\ub294 \/)\uc774\ub2e4. \ub808\uc774\uc800\uac00 \uac00\uc7a5 \uc544\ub7ab \ud589\uc758 \uc624\ub978\ucabd\uc73c\ub85c \ube60\uc838 \ub098\uc62c \ub54c(\uc67c\ucabd \uadf8\ub9bc), \uae08\uace0\uac00 \uc5f4\ub9b0\ub2e4. \uadf8 \uc678\uc758 \uacbd\uc6b0\uc5d0\ub294 \uc54c\ub78c\uc774 \uc6b8\ub9b0\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 \uae08\uace0\uc5d0\ub294 \uac70\uc6b8\uc774 \ud55c \uac1c\uc529 \ube60\uc838\uc788\ub2e4. (\uc624\ub978\ucabd \uadf8\ub9bc) \uc0ac\uc6a9\uc790\ub294 \uac70\uc6b8 \ud55c \uac1c\ub97c \ube44\uc5b4\uc788\ub294 \uce78\uc5d0 \ub123\ub294\ub2e4. \uc62c\ubc14\ub978 \uc0ac\uc6a9\uc790\ub294 \uac70\uc6b8\uc758 \uc815\ud655\ud55c \uc704\uce58\uc640 \ubaa8\uc591 (4\ud589 3\uc5f4, \/)\uc744 \uc54c\uace0 \uc788\uae30 \ub54c\ubb38\uc5d0, \uae08\uace0\ub97c \uc548\uc804\ud558\uac8c \uc5f4 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uae08\uace0\uc758 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uae08\uace0\uac00 \uc548\uc804\ud55c\uc9c0 \uc544\ub2cc\uc9c0 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624. \uc548\uc804\ud55c \uae08\uace0\ub294 \uac70\uc6b8\uc744 \ub123\uc9c0 \uc54a\uc558\uc744 \ub54c \uc5f4\ub9ac\uba74 \uc548\ub418\uba70, \uae08\uace0\ub97c \uc5f4 \uc218 \uc788\ub294 \uac70\uc6b8\uc758 \uc704\uce58\uc640 \ubaa8\uc591\uc774 \uc801\uc5b4\ub3c4 \ud55c \uac1c\ub294 \uc874\uc7ac\ud55c\ub2e4.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \uc5ec\ub7ec \uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uace0 \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \uae08\uace0 \ud558\ub098\ub97c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n\r\n<p>\ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 \ub124\uc815\uc218 r, c, m, n\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; r,c &le; 1,000,000, 0 &le; m,n &le; 200,000) \uae08\uace0\ub294 r\ud589 c\uc5f4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c m\uac1c \uc904\uc5d0\ub294 \ub450 \uc815\uc218 r<sub>i<\/sub>\uc640 c<sub>i<\/sub> (1 &le; r<sub>i<\/sub> &le; r, 1 &le; c<sub>i<\/sub> &le; c)\uac00 \uc8fc\uc5b4\uc9c0\uba70, r<sub>i<\/sub>\ud589 c<sub>i<\/sub> \uc5f4\uc5d0 \/\ubaa8\uc591\uc758 \uac70\uc6b8\uc774 \uc788\ub2e4\ub294 \ub73b\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c n\uac1c \uc904\uc5d0\ub3c4 \\\ubaa8\uc591&nbsp;\uac70\uc6b8\uc758 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9c0\uba70, \/\ubaa8\uc591 \uc815\ubcf4\uc640 \uac19\uc740 \ubc29\uc2dd\uc73c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 m+n\uac1c\uc758 \uc704\uce58\ub294 \uc11c\ub85c \ub2e4\ub974\ub2e4.&nbsp;<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4, \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 \ubc88\ud638\ub97c \ucd9c\ub825\ud558\uace0 \ub2e4\uc74c\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li><code>0<\/code> \uac70\uc6b8\uc744 \uc0bd\uc785\ud558\uc9c0 \uc54a\uace0 \uae08\uace0\ub97c \uc5f4 \uc218 \uc788\uc744\ub54c<\/li>\r\n\t<li><code>k r c<\/code> \uac70\uc6b8\uc744 \ub123\uc9c0 \uc54a\uc73c\uba74 \uae08\uace0\uac00 \uc5f4\ub9ac\uc9c0 \uc54a\uace0, \uae08\uace0\ub97c \uc5f4 \uc218 \uc788\ub294 \uc704\uce58\uc758 \uc218\uac00 k\uac1c, \uadf8 \uc911 \uac00\uc7a5 \uc0ac\uc804\uc21c\uc73c\ub85c \uc55e\uc11c\ub294 \uc704\uce58\uac00 (r, c)\uc778 \uacbd\uc6b0 (\ud55c \uc704\uce58\uc5d0 \/\uc640 \\ \ubaa8\uc591\uc758 \uac70\uc6b8\uc744 \ub123\uc744 \uc218 \uc788\ub294 \uacbd\uc6b0\uc5d0 \uc704\uce58 1\uac1c\ub85c \uc13c\ub2e4)<\/li>\r\n\t<li><code>impossible<\/code> \uac70\uc6b8\uc744 \ub123\uc5b4\ub3c4 \uae08\uace0\ub97c \uc5f4 \uc218 \uc5c6\ub294 \uacbd\uc6b0<\/li>\r\n<\/ul>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"4211","problem_lang":"1","title":"A Safe Bet","description":"<p>Safe Ltd. is a company that manufactures high-quality safes. Its latest invention is an optical closure mechanism that uses a laser beam passing through a rectangular grid with several mirrors.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/mirro.png\" style=\"height:178px; width:600px\" \/><\/p>\r\n\r\n<p>When the laser is activated, a beam enters the top row of the grid horizontally from the left. The beam is reflected by every mirror that it hits. Each mirror has a 45 degree diagonal orientation, either \/ or \\. If the beam exits the bottom row of the grid horizontally to the right, it is detected and the safe opens (see the left side of the \ufb01gure above). Otherwise the safe remains closed and an alarm is raised.&nbsp;<\/p>\r\n\r\n<p>Each safe has a missing mirror, which prevents the laser beam from traveling successfully through the grid (see the right side of the \ufb01gure above). The safe has a mechanism that enables the user to drop a single mirror into any empty grid cell. A legitimate user knows the correct position and orientation of the missing mirror (\/ in row 4 column 3 above) and can thus open the safe. Without this knowledge the user has to guess correctly, which can be dif\ufb01cult for safes with large grids.&nbsp;<\/p>\r\n\r\n<p>Your job is to determine if particular safes are actually secure. A secure safe does not open right away without inserting a mirror, and there is at least one valid location and orientation for the missing mirror. There may indeed be multiple such locations and orientations.<\/p>\r\n","input":"<p>Each test case describes a single safe and starts with a line containing four integer numbers r, c, m, and n (1 &le; r, c &le; 1 000 000 and 0 &le; m, n &le; 200 000). The mechanism&rsquo;s grid has r rows and c columns. Each of the next m lines contains two integer numbers r<sub>i<\/sub> and c<sub>i<\/sub> (1 &le; r<sub>i<\/sub> &le; r and 1 &le; c<sub>i<\/sub> &le; c) specifying that there is a \/ mirror in row r<sub>i<\/sub> column c<sub>i<\/sub>. The following n lines specify the positions of the \\ mirrors in the same way. The m + n positions of the mirrors are pairwise distinct.<\/p>\r\n","output":"<p>For each test case, display its case number followed by:<\/p>\r\n\r\n<ul>\r\n\t<li><code>0<\/code> if the safe opens without inserting a mirror.<\/li>\r\n\t<li><code>k r c<\/code> if the safe does not open without inserting a mirror, there are exactly k positions where inserting a mirror opens the safe, and (r, c) is the lexicographically smallest such row, column position. A position where both a \/ and a \\ mirror open the safe counts just once.<\/li>\r\n\t<li><code>impossible<\/code> if the safe cannot be opened with or without inserting a mirror.<\/li>\r\n<\/ul>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

ICPC > World Finals > ACM-ICPC World Finals 2012 I번