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문제

농부 John은 자기 집을 좀 더 꾸밀 필요가 있다고 생각했습니다. 중국 물품 가게에 갔다가 그는 섬세한 유리 소 장식품을 발견했고, 벽난로 선반에 놓으면 딱 적당할 것 같아서 그만 구매하기로 했습니다.

소 장식품의 모양은 아래에 나와있는 것처럼 (3 <= N, M <= 500) 인 N x M 형태의 문자 배열로 적혀있고, 소문자 영어가 (각각이 다른 색인) 장식품의 각 부분을 나타냅니다. '.' 기호는 아무것도 없는 빈 공간입니다.

...............
...............
x..x...........
xxxx...........
xxxxaaaaaaa...
.xx.aaaaaaaaa..
....aaaaaaa.aa.
....ll...ll....
....vv...vv....
...............

안타깝게도 농부 John이 이 장식품을 구매하기 바로 직전에 이놈의 황소가 가게를 가로질러 날아가더니, 농부 John이 사기로 했던 장식물 말고도 선반에 있던 다른 여러 장식물까지 박살내버렸네요! 농부 John의 조각상은 3조각으로 나뉘었는데, 결국 바닥에 떨어져있는 (4 <= K <= 100)인 모두 K개의 조각들 사이에 섞여서 사라져버렸네요. 각 조각은 위의 소 조각상처럼 문자 배열로 적혀있습니다.

농부 John이 (바닥에 떨어진 K조각 중) 다시 이어붙여 소로 만들 수 있는 3조각의 조합을 얼마나 만들 수 있는지 파악하도록 도와주세요.

바닥에 떨어진 조각은 가로로 혹은 세로로 뒤집어져 있거나, 90도씩 회전되어 있을 수 있습니다. 그래서 K개의 주어진 조각의 배열에서, 원래 모양대로 만들 수 있는 3개의 조각의 조합을 찾기 위해, 조각을 이동하거나, 뒤집거나, 90도씩 회전할 수 있습니다. 그렇게 조각들을 놓았을 때, 놓여진 3조각이 각각의 원래 조각과 색상까지 완전히 동일하게 일치해야 합니다.

입력

입력의 첫 번째 줄은 단일 정수 K가 주어집니다. 다음 줄부터는 K + 1개의 조각을 설명합니다. 첫 번째 조각은 원래 소 장식품의 모양이 기술되고, 다음 줄 부터는 K개의 조각들의 모양을 설명합니다.

각각의 조각 설명은 두 정수 R, C (1 <= R, C <= 100) 이 적혀있는 줄로 시작합니다. 뒤따라 나오는 R개의 줄에는 각 칸의 색을 표현하는 한 줄에 C개씩의 소문자 알파벳이 나옵니다. 각 조각은 수직 / 수평으로 이어져있고 적어도 하나의 비어있는 칸이 있습니다.

출력

원래 조각을 만들 수 있는 조각 i, j, k (i < j < k)의 조합의 개수를 출력하세요.

예제 입력 1

5
5 5
aaaaa
..a..
bbabb
..a..
aaaaa
3 5
..abb
..a..
aaaaa
5 2
a.
a.
aa
a.
a.
1 2
bb
1 5
bbabb
2 5
aaaaa
..a..

예제 출력 1

3

힌트

세 해결방법은 조각 (0, 1, 2), (0, 2, 4), (1, 3, 4) 를 사용합니다.

[{"problem_id":"12009","problem_lang":"0","title":"\uc911\uad6d \uc7a1\ub3d9\uc0ac\ub2c8 \uac00\uac8c\uc758 \uc18c \uc7a5\uc2dd\ud488 (Platinum)","description":"<p>\ub18d\ubd80 John\uc740 \uc790\uae30 \uc9d1\uc744 \uc880 \ub354 \uafb8\ubc00 \ud544\uc694\uac00 \uc788\ub2e4\uace0 \uc0dd\uac01\ud588\uc2b5\ub2c8\ub2e4. \uc911\uad6d \ubb3c\ud488 \uac00\uac8c\uc5d0 \uac14\ub2e4\uac00 \uadf8\ub294 \uc12c\uc138\ud55c \uc720\ub9ac \uc18c \uc7a5\uc2dd\ud488\uc744 \ubc1c\uacac\ud588\uace0, \ubcbd\ub09c\ub85c \uc120\ubc18\uc5d0 \ub193\uc73c\uba74 \ub531 \uc801\ub2f9\ud560 \uac83 \uac19\uc544\uc11c \uadf8\ub9cc \uad6c\ub9e4\ud558\uae30\ub85c \ud588\uc2b5\ub2c8\ub2e4.<\/p>\r\n\r\n<p>\uc18c \uc7a5\uc2dd\ud488\uc758 \ubaa8\uc591\uc740 \uc544\ub798\uc5d0 \ub098\uc640\uc788\ub294 \uac83\ucc98\ub7fc (3 &lt;= N, M &lt;= 500) \uc778 N x M \ud615\ud0dc\uc758 \ubb38\uc790 \ubc30\uc5f4\ub85c \uc801\ud600\uc788\uace0, \uc18c\ubb38\uc790 \uc601\uc5b4\uac00 (\uac01\uac01\uc774 \ub2e4\ub978 \uc0c9\uc778) \uc7a5\uc2dd\ud488\uc758 \uac01 \ubd80\ubd84\uc744 \ub098\ud0c0\ub0c5\ub2c8\ub2e4. &#39;.&#39; \uae30\ud638\ub294 \uc544\ubb34\uac83\ub3c4 \uc5c6\ub294 \ube48 \uacf5\uac04\uc785\ub2c8\ub2e4.<\/p>\r\n\r\n<pre>\r\n...............\r\n...............\r\nx..x...........\r\nxxxx...........\r\nxxxxaaaaaaa...\r\n.xx.aaaaaaaaa..\r\n....aaaaaaa.aa.\r\n....ll...ll....\r\n....vv...vv....\r\n...............\r\n<\/pre>\r\n\r\n<p>\uc548\ud0c0\uae5d\uac8c\ub3c4 \ub18d\ubd80 John\uc774 \uc774 \uc7a5\uc2dd\ud488\uc744 \uad6c\ub9e4\ud558\uae30 \ubc14\ub85c \uc9c1\uc804\uc5d0 \uc774\ub188\uc758 \ud669\uc18c\uac00 \uac00\uac8c\ub97c \uac00\ub85c\uc9c8\ub7ec \ub0a0\uc544\uac00\ub354\ub2c8, \ub18d\ubd80 John\uc774 \uc0ac\uae30\ub85c \ud588\ub358 \uc7a5\uc2dd\ubb3c \ub9d0\uace0\ub3c4 \uc120\ubc18\uc5d0 \uc788\ub358 \ub2e4\ub978 \uc5ec\ub7ec \uc7a5\uc2dd\ubb3c\uae4c\uc9c0 \ubc15\uc0b4\ub0b4\ubc84\ub838\ub124\uc694! \ub18d\ubd80 John\uc758 \uc870\uac01\uc0c1\uc740 3\uc870\uac01\uc73c\ub85c \ub098\ub258\uc5c8\ub294\ub370, \uacb0\uad6d \ubc14\ub2e5\uc5d0 \ub5a8\uc5b4\uc838\uc788\ub294 (4 &lt;= K &lt;= 100)\uc778 \ubaa8\ub450 K\uac1c\uc758 \uc870\uac01\ub4e4 \uc0ac\uc774\uc5d0 \uc11e\uc5ec\uc11c \uc0ac\ub77c\uc838\ubc84\ub838\ub124\uc694. \uac01 \uc870\uac01\uc740 \uc704\uc758 \uc18c \uc870\uac01\uc0c1\ucc98\ub7fc \ubb38\uc790 \ubc30\uc5f4\ub85c \uc801\ud600\uc788\uc2b5\ub2c8\ub2e4.<\/p>\r\n\r\n<p>\ub18d\ubd80 John\uc774 (\ubc14\ub2e5\uc5d0 \ub5a8\uc5b4\uc9c4 K\uc870\uac01 \uc911) \ub2e4\uc2dc \uc774\uc5b4\ubd99\uc5ec \uc18c\ub85c \ub9cc\ub4e4 \uc218 \uc788\ub294 3\uc870\uac01\uc758 \uc870\ud569\uc744 \uc5bc\ub9c8\ub098 \ub9cc\ub4e4 \uc218 \uc788\ub294\uc9c0 \ud30c\uc545\ud558\ub3c4\ub85d \ub3c4\uc640\uc8fc\uc138\uc694.<\/p>\r\n\r\n<p>\ubc14\ub2e5\uc5d0 \ub5a8\uc5b4\uc9c4 \uc870\uac01\uc740 \uac00\ub85c\ub85c \ud639\uc740 \uc138\ub85c\ub85c \ub4a4\uc9d1\uc5b4\uc838 \uc788\uac70\ub098, 90\ub3c4\uc529 \ud68c\uc804\ub418\uc5b4 \uc788\uc744 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uadf8\ub798\uc11c K\uac1c\uc758 \uc8fc\uc5b4\uc9c4 \uc870\uac01\uc758 \ubc30\uc5f4\uc5d0\uc11c, \uc6d0\ub798 \ubaa8\uc591\ub300\ub85c \ub9cc\ub4e4 \uc218 \uc788\ub294 3\uac1c\uc758 \uc870\uac01\uc758 \uc870\ud569\uc744 \ucc3e\uae30 \uc704\ud574, \uc870\uac01\uc744 \uc774\ub3d9\ud558\uac70\ub098, \ub4a4\uc9d1\uac70\ub098, 90\ub3c4\uc529 \ud68c\uc804\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uadf8\ub807\uac8c \uc870\uac01\ub4e4\uc744 \ub193\uc558\uc744 \ub54c, \ub193\uc5ec\uc9c4 3\uc870\uac01\uc774 \uac01\uac01\uc758 \uc6d0\ub798 \uc870\uac01\uacfc \uc0c9\uc0c1\uae4c\uc9c0 \uc644\uc804\ud788 \ub3d9\uc77c\ud558\uac8c \uc77c\uce58\ud574\uc57c \ud569\ub2c8\ub2e4.<\/p>\r\n","input":"<p>\uc785\ub825\uc758 \uccab \ubc88\uc9f8 \uc904\uc740 \ub2e8\uc77c \uc815\uc218 K\uac00 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. \ub2e4\uc74c \uc904\ubd80\ud130\ub294 K + 1\uac1c\uc758 \uc870\uac01\uc744 \uc124\uba85\ud569\ub2c8\ub2e4. \uccab \ubc88\uc9f8 \uc870\uac01\uc740 \uc6d0\ub798 \uc18c \uc7a5\uc2dd\ud488\uc758 \ubaa8\uc591\uc774 \uae30\uc220\ub418\uace0, \ub2e4\uc74c \uc904 \ubd80\ud130\ub294 K\uac1c\uc758 \uc870\uac01\ub4e4\uc758 \ubaa8\uc591\uc744 \uc124\uba85\ud569\ub2c8\ub2e4.<\/p>\r\n\r\n<p>\uac01\uac01\uc758 \uc870\uac01 \uc124\uba85\uc740 \ub450 \uc815\uc218 R, C (1 &lt;= R, C &lt;= 100) \uc774 \uc801\ud600\uc788\ub294 \uc904\ub85c \uc2dc\uc791\ud569\ub2c8\ub2e4. \ub4a4\ub530\ub77c \ub098\uc624\ub294 R\uac1c\uc758 \uc904\uc5d0\ub294 \uac01 \uce78\uc758 \uc0c9\uc744 \ud45c\ud604\ud558\ub294 \ud55c \uc904\uc5d0 C\uac1c\uc529\uc758 \uc18c\ubb38\uc790 \uc54c\ud30c\ubcb3\uc774 \ub098\uc635\ub2c8\ub2e4. \uac01 \uc870\uac01\uc740 \uc218\uc9c1 \/ \uc218\ud3c9\uc73c\ub85c \uc774\uc5b4\uc838\uc788\uace0 \uc801\uc5b4\ub3c4 \ud558\ub098\uc758 \ube44\uc5b4\uc788\ub294 \uce78\uc774 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\r\n","output":"<p>\uc6d0\ub798 \uc870\uac01\uc744 \ub9cc\ub4e4 \uc218 \uc788\ub294 \uc870\uac01 i, j, k (i &lt; j &lt; k)\uc758 \uc870\ud569\uc758 \uac1c\uc218\ub97c \ucd9c\ub825\ud558\uc138\uc694.<\/p>\r\n","hint":"<p>\uc138 \ud574\uacb0\ubc29\ubc95\uc740 \uc870\uac01 (0, 1, 2), (0, 2, 4), (1, 3, 4) \ub97c \uc0ac\uc6a9\ud569\ub2c8\ub2e4.<\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"12009","problem_lang":"1","title":"Bull in a China Shop (Platinum)","description":"<p>Farmer John has decided his home needs more decoration. Visiting the local china shop, he finds a delicate glass cow figurine that he decides to purchase, knowing that it will fit perfectly on the mantel above his fireplace.<\/p>\r\n\r\n<p>The shape of the cow figurine is described by an \\(N \\times M\\) grid of characters like the one below (\\(3 \\leq N, M \\leq 500\\)), where lowercase letter characters are each part of the figurine (indicating different colors) and &#39;.&#39; characters are not.<\/p>\r\n\r\n<pre>\r\n...............\r\n...............\r\nx..x...........\r\nxxxx...........\r\nxxxxaaaaaaa...\r\n.xx.aaaaaaaaa..\r\n....aaaaaaa.aa.\r\n....ll...ll....\r\n....vv...vv....\r\n...............\r\n<\/pre>\r\n\r\n<p>Unfortunately, right before FJ can make his purchase, a bull runs through the shop and breaks not only FJ&#39;s figurine, but many of the other glass objects on the shelves as well! FJ&#39;s figurine breaks into 3 pieces, which quickly become lost among \\(K\\) total pieces lying on the ground (\\(4 \\leq K \\leq 100\\)). Each of the \\(K\\) pieces is described by a grid of characters, just like the original figurine.<\/p>\r\n\r\n<p>Please help FJ determine how many sets of 3 pieces (out of the \\(K\\) on the floor) could be glued back together to mend his broken figurine.<\/p>\r\n\r\n<p>The pieces on the ground might have been flipped vertically or horizontally, or rotated by some multiple of 90 degrees. Therefore, given the original grid as well as \\(K\\) grids describing pieces, you want to find sets of 3 pieces that can be joined together to form the original picture, allowing the pieces to be translated, flipped, or rotated multiples of 90 degrees. When then superimposed, the 3 pieces should exactly form the original picture, with each colored square in the original picture represented in exactly one of the pieces.<\/p>\r\n","input":"<p>The first line contains a single integer \\(K\\). Following that will be \\(K + 1\\) piece descriptions. The first description will describe the original glass cow, the following \\(K\\) descriptions will be of the broken pieces.<\/p>\r\n\r\n<p>Each description begins with a line containing two integers \\(R\\) and \\(C\\) (\\(1 \\le R, C \\le 100\\)). The following \\(R\\) lines contain \\(C\\) lowercase alphabet characters describing the color of each cell. Each piece will be horizontally\/vertically connected and have at least one non-empty cell.<\/p>\r\n","output":"<p>Output the number of triples \\(i, j, k\\) (\\(i &lt; j &lt; k\\)) such that pieces \\(i\\), \\(j\\), and \\(k\\) can be arranged to form the original glass cow.<\/p>\r\n","hint":"<p>The three solutions use pieces \\((0, 1, 2)\\), \\((0, 2, 4)\\), \\((1, 3, 4)\\).<\/p>\r\n\r\n<p>Note that this problem has a time limit of 6 seconds per test case (and twice that for Java and Python submissions).<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

Olympiad > USA Computing Olympiad > 2015-2016 Season > USACO US Open 2016 Contest > Platinum 2번

  • 문제의 오타를 찾은 사람: ntopia
  • 문제를 번역한 사람: sftblw