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문제

상근이의 농장은 매우 넓기 때문에, 어떤 곳에 어떤 식물을 심었는지를 기록해 놔야 한다. 상근이는 기록을 위해 인터넷 쇼핑몰에서 고화질 지도를 주문했다. 지도는 매우 크기 때문에, 종이 한 장이 인쇄할 수 없다. 따라서, 지도를 쪼개 종이 여러 장에 인쇄를 해야 한다.

동일한 지도를 어떻게 놓느냐에 따라 필요한 종이의 개수가 달라질 수도 있다. 상근이의 정원의 지도와 종이의 크기가 주어졌을 때, 지도를 인쇄하는데 필요한 종이 개수의 최소값을 구하는 프로그램을 작성하시오.

위의 그림은 텍사스처럼 생긴 지도를 인쇄하는 두 가지 방법이다. 첫 번째 그림은 종이 14개로 인쇄하는 방법이고, 오른쪽은 같은 지도를 동일한 종이 10개로 인쇄하는 방법이다.

종이의 변은 모두 x축과 y축에 평행해야 한다. 또, 종이는 회전시킬 수 없고, 두 종이가 전체 변을 공유하는 경우에만 접할 수 있다.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다. 각 테스트 케이스의 첫째 줄에는 Ar, Ac, Tr, Tc가 주어진다. Ar과 Ac는 지도의 픽셀 개수이고, Tr과 Tc는 종이 한 장에 인쇄할 수 있는 픽셀의 개수이다. (1 ≤ Ax ≤ 1000, 1 ≤ Tx ≤ 100) 다음 Ar개 줄에는 Ac개의 문자가 주어진다. 'X'는 상근이의 농장, '.'는 상근이의 농장이 아닌 곳이다.

모든 X를 종이에 인쇄해야 하며, 지도의 'X'는 모두 같은 영역에 속한다.

출력

각 테스트 케이스마다, 모든 'X'를 종이에 인쇄하는데 필요한 종이 개수의 최소값을 출력한다.

예제 입력 1

3 3 2 2
XXX
XXX
XXX
3 3 2 2
XX.
XXX
XXX
17 32 5 9
........XXXXXXXX................
........XXXXXXXX................
........XXXXXXXX................
........XXXXXXXXX...............
........XXXXXXXXXXXXXXX.........
........XXXXXXXXXXXXXXXXXXXX....
........XXXXXXXXXXXXXXXXXXXXX...
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX..
..XXXXXXXXXXXXXXXXXXXXXXXXXXXXX.
....XXXXXXXXXXXXXXXXXXXXXXXXXXX.
......XXXXXXXXXXXXXXXXXXXXXXXXX.
........XX..XXXXXXXXXXXXXXXXX...
.............XXXXXXXXXXXXXX.....
...............XXXXXXXXX........
................XXXXXXX.........
.................XXXXX..........
....................XXX.........

예제 출력 1

4
3
10
[{"problem_id":"9274","problem_lang":"0","title":"\uc885\uc774 \uc9c0\ub3c4","description":"<p>\uc0c1\uadfc\uc774\uc758 \ub18d\uc7a5\uc740 \ub9e4\uc6b0 \ub113\uae30 \ub54c\ubb38\uc5d0, \uc5b4\ub5a4 \uacf3\uc5d0 \uc5b4\ub5a4 \uc2dd\ubb3c\uc744 \uc2ec\uc5c8\ub294\uc9c0\ub97c \uae30\ub85d\ud574 \ub194\uc57c \ud55c\ub2e4. \uc0c1\uadfc\uc774\ub294 \uae30\ub85d\uc744 \uc704\ud574 \uc778\ud130\ub137 \uc1fc\ud551\ubab0\uc5d0\uc11c \uace0\ud654\uc9c8 \uc9c0\ub3c4\ub97c \uc8fc\ubb38\ud588\ub2e4. \uc9c0\ub3c4\ub294 \ub9e4\uc6b0 \ud06c\uae30 \ub54c\ubb38\uc5d0, \uc885\uc774 \ud55c \uc7a5\uc774 \uc778\uc1c4\ud560 \uc218 \uc5c6\ub2e4. \ub530\ub77c\uc11c, \uc9c0\ub3c4\ub97c \ucabc\uac1c \uc885\uc774 \uc5ec\ub7ec \uc7a5\uc5d0 \uc778\uc1c4\ub97c \ud574\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub3d9\uc77c\ud55c \uc9c0\ub3c4\ub97c \uc5b4\ub5bb\uac8c \ub193\ub290\ub0d0\uc5d0 \ub530\ub77c \ud544\uc694\ud55c \uc885\uc774\uc758 \uac1c\uc218\uac00 \ub2ec\ub77c\uc9c8 \uc218\ub3c4 \uc788\ub2e4. \uc0c1\uadfc\uc774\uc758 \uc815\uc6d0\uc758 \uc9c0\ub3c4\uc640 \uc885\uc774\uc758 \ud06c\uae30\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc9c0\ub3c4\ub97c \uc778\uc1c4\ud558\ub294\ub370 \ud544\uc694\ud55c \uc885\uc774 \uac1c\uc218\uc758 \ucd5c\uc18c\uac12\uc744 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/fmap.png\" style=\"height:210px; line-height:1.6em; opacity:0.9; width:457px\" \/><\/p>\r\n\r\n<p>\uc704\uc758 \uadf8\ub9bc\uc740 \ud14d\uc0ac\uc2a4\ucc98\ub7fc \uc0dd\uae34 \uc9c0\ub3c4\ub97c \uc778\uc1c4\ud558\ub294 \ub450 \uac00\uc9c0 \ubc29\ubc95\uc774\ub2e4. \uccab \ubc88\uc9f8 \uadf8\ub9bc\uc740 \uc885\uc774 14\uac1c\ub85c \uc778\uc1c4\ud558\ub294 \ubc29\ubc95\uc774\uace0, \uc624\ub978\ucabd\uc740 \uac19\uc740 \uc9c0\ub3c4\ub97c \ub3d9\uc77c\ud55c \uc885\uc774 10\uac1c\ub85c \uc778\uc1c4\ud558\ub294 \ubc29\ubc95\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc885\uc774\uc758 \ubcc0\uc740 \ubaa8\ub450 x\ucd95\uacfc y\ucd95\uc5d0 \ud3c9\ud589\ud574\uc57c \ud55c\ub2e4. \ub610, \uc885\uc774\ub294 \ud68c\uc804\uc2dc\ud0ac \uc218 \uc5c6\uace0, \ub450 \uc885\uc774\uac00 \uc804\uccb4 \ubcc0\uc744 \uacf5\uc720\ud558\ub294 \uacbd\uc6b0\uc5d0\ub9cc \uc811\ud560 \uc218 \uc788\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\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 A<sub>r<\/sub>, A<sub>c<\/sub>, T<sub>r<\/sub>, T<sub>c<\/sub>\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. A<sub>r<\/sub>\uacfc A<sub>c<\/sub>\ub294 \uc9c0\ub3c4\uc758 \ud53d\uc140 \uac1c\uc218\uc774\uace0, T<sub>r<\/sub>\uacfc T<sub>c<\/sub>\ub294 \uc885\uc774 \ud55c \uc7a5\uc5d0 \uc778\uc1c4\ud560 \uc218 \uc788\ub294 \ud53d\uc140\uc758 \uac1c\uc218\uc774\ub2e4. (1 &le; A<sub>x<\/sub> &le; 1000, 1 &le; T<sub>x<\/sub> &le; 100) \ub2e4\uc74c Ar\uac1c \uc904\uc5d0\ub294 Ac\uac1c\uc758 \ubb38\uc790\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. &#39;X&#39;\ub294 \uc0c1\uadfc\uc774\uc758 \ub18d\uc7a5, &#39;.&#39;\ub294 \uc0c1\uadfc\uc774\uc758 \ub18d\uc7a5\uc774 \uc544\ub2cc \uacf3\uc774\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 X\ub97c \uc885\uc774\uc5d0 \uc778\uc1c4\ud574\uc57c \ud558\uba70, \uc9c0\ub3c4\uc758 &#39;X&#39;\ub294 \ubaa8\ub450 \uac19\uc740 \uc601\uc5ed\uc5d0 \uc18d\ud55c\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4, \ubaa8\ub4e0 &#39;X&#39;\ub97c \uc885\uc774\uc5d0 \uc778\uc1c4\ud558\ub294\ub370 \ud544\uc694\ud55c \uc885\uc774 \uac1c\uc218\uc758 \ucd5c\uc18c\uac12\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"9274","problem_lang":"1","title":"Folded Map","description":"<p>Freddy&rsquo;s garden became so large that he needs a map to keep evidence of which vegetables are planted in what area. He ordered a high-quality map from the International Cartographic Publishing Company (ICPC). Since the map has a large scale, it does not \ufb01t onto a single page and it has to be split into several rectangular tiles.<\/p>\r\n\r\n<p>Even with a \ufb01xed tile size (determined by a page size) and map scale, the number of tiles may still di\ufb00er by adjusting the position of the tile grid. Your task is to \ufb01nd the minimal number of tiles necessary to cover the whole region of Freddy&rsquo;s garden.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/fmap.png\" style=\"height:210px; width:457px\" \/><\/p>\r\n\r\n<p>Two of many possible ways of tiling Texas-shaped region<\/p>\r\n\r\n<p>Let&rsquo;s have a look at an example. The \ufb01gure on the left shows 14 map tiles covering a region. By adjusting the grid position a little bit, we may cover the same region with only 10 tiles, without changing their size or orientation.<\/p>\r\n\r\n<p>Note that the tiles must be part of a rectangular grid aligned with the x-axis and y-axis. That is, they touch each other only with their whole sides and cannot be rotated.<\/p>\r\n","input":"<p>The input contains several test cases. The \ufb01rst line of each test case contains four integer numbers: A<sub>r<\/sub>, A<sub>c<\/sub>, T<sub>r<\/sub>, and T<sub>c<\/sub>. A<sub>r<\/sub> and A<sub>c<\/sub> give the input image resolution in pixels (1 &le; A<sub>x<\/sub> &le; 1000), while T<sub>r<\/sub> and T<sub>c<\/sub> is the size of one tile in pixels (1 &le; T<sub>x<\/sub> &le; 100). The next A<sub>r<\/sub> lines each contain A<sub>c<\/sub> characters, each of them being either &ldquo;X&rdquo; (the pixel corresponds to a part of the garden to be covered by a tile) or &ldquo;.&rdquo; (the corresponding pixel is outside the garden and does not need to be covered). The region pixels form one connected region.<\/p>\r\n","output":"<p>For each test case, print one integer number &mdash; the minimal number of tiles necessary to cover all pixels represented by &ldquo;X&rdquo;.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]