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문제

지도를 만드는 일은 쉬운 일이 아니다. 지구는 구형이기 때문에, 2차원 평면에 나타낼 때 왜곡이 발생한다. 또, 고화질 지도는 매우 크기 때문에, 종이 한장에 인쇄할 수 없다. 따라서, 지도를 여러 부분으로 쪼갠 나눈 다음 종이 여러 개에 인쇄를 해 합친다.

상근이는 지도를 제작하고 있다. 상근이는 항상 이익만을 추구하기 때문에, 종이를 최대한 적게 사용해 지도를 인쇄하려고 한다. 종이의 크기는 모두 같다.

왼쪽 그림은 한 지도를 종이 14개에 인쇄한 것이고, 오른쪽 그림은 같은 지도를 종이 10개에 인쇄한 것이다. 두 지도 모두 같은 종이를 사용하며, 종이의 크기와 방향은 모두 같다.

지도가 주어졌을 때, 지도를 인쇄하는데 필요한 종이 개수의 최소값을 구하는 프로그램을 작성하시오. 지도는 모두 닫힌 다각형이고, 교차하지 않는다.

종이는 모두 직사각형이고, x축과 y축에 평행해야 한다. 서로 접하는 종이의 꼭지점은 일치해야 하고, 종이를 회전할 수는 없다. 입력으로 주어지는 모든 좌표는 정수이지만, 종이는 정수가 아닌 좌표에 놓을 수 있다.

지도는 종이의 외각선에 접해도 된다. 소수점 계산으로 생기는 오차를 피하기 위해, 지도가 종이의 바깥으로 10-6 까지 넘어가도 정답은 같다.

입력

첫째 줄에 지도의 꼭지점의 수 n (3 ≤ n ≤ 50), 종이의 크기 xs, ys (1 ≤ xs, ys ≤ 100)이 주어진다.

다음 n개 줄에는 지도의 꼭지점을 나타내는 두 정수 x와 y가 주어진다. (0 ≤ x ≤ 10xs, 0 ≤ y ≤ 10ys) 꼭지점은 시계방향 또는 반시계방향으로 주어진다.

출력

첫째 줄에 지도를 인쇄하기 위해 필요한 종이 개수의 최소값을 출력한다.

예제 입력 1

12 9 9
1 8
1 16
6 16
9 29
19 31
23 24
30 23
29 18
20 12
22 8
14 0
14 8

예제 출력 1

10

힌트

[{"problem_id":"8883","problem_lang":"0","title":"\uc885\uc774 \uc9c0\ub3c4","description":"<p>\uc9c0\ub3c4\ub97c \ub9cc\ub4dc\ub294 \uc77c\uc740 \uc26c\uc6b4 \uc77c\uc774 \uc544\ub2c8\ub2e4. \uc9c0\uad6c\ub294 \uad6c\ud615\uc774\uae30 \ub54c\ubb38\uc5d0, 2\ucc28\uc6d0 \ud3c9\uba74\uc5d0 \ub098\ud0c0\ub0bc \ub54c \uc65c\uace1\uc774 \ubc1c\uc0dd\ud55c\ub2e4. \ub610, \uace0\ud654\uc9c8 \uc9c0\ub3c4\ub294 \ub9e4\uc6b0 \ud06c\uae30 \ub54c\ubb38\uc5d0, \uc885\uc774 \ud55c\uc7a5\uc5d0 \uc778\uc1c4\ud560 \uc218 \uc5c6\ub2e4. \ub530\ub77c\uc11c, \uc9c0\ub3c4\ub97c \uc5ec\ub7ec \ubd80\ubd84\uc73c\ub85c \ucabc\uac20 \ub098\ub208 \ub2e4\uc74c \uc885\uc774 \uc5ec\ub7ec \uac1c\uc5d0 \uc778\uc1c4\ub97c \ud574 \ud569\uce5c\ub2e4.<\/p>\r\n\r\n<p>\uc0c1\uadfc\uc774\ub294 \uc9c0\ub3c4\ub97c \uc81c\uc791\ud558\uace0 \uc788\ub2e4. \uc0c1\uadfc\uc774\ub294 \ud56d\uc0c1 \uc774\uc775\ub9cc\uc744 \ucd94\uad6c\ud558\uae30 \ub54c\ubb38\uc5d0, \uc885\uc774\ub97c \ucd5c\ub300\ud55c \uc801\uac8c \uc0ac\uc6a9\ud574 \uc9c0\ub3c4\ub97c \uc778\uc1c4\ud558\ub824\uace0 \ud55c\ub2e4. \uc885\uc774\uc758 \ud06c\uae30\ub294 \ubaa8\ub450 \uac19\ub2e4.<\/p>\r\n\r\n<p>\uc67c\ucabd \uadf8\ub9bc\uc740 \ud55c \uc9c0\ub3c4\ub97c \uc885\uc774 14\uac1c\uc5d0 \uc778\uc1c4\ud55c \uac83\uc774\uace0, \uc624\ub978\ucabd \uadf8\ub9bc\uc740 \uac19\uc740 \uc9c0\ub3c4\ub97c \uc885\uc774 10\uac1c\uc5d0 \uc778\uc1c4\ud55c \uac83\uc774\ub2e4. \ub450 \uc9c0\ub3c4 \ubaa8\ub450 \uac19\uc740 \uc885\uc774\ub97c \uc0ac\uc6a9\ud558\uba70, \uc885\uc774\uc758 \ud06c\uae30\uc640 \ubc29\ud5a5\uc740 \ubaa8\ub450 \uac19\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/tile(2).png\" style=\"height:220px; width:395px\" \/><\/p>\r\n\r\n<p>\uc9c0\ub3c4\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. \uc9c0\ub3c4\ub294 \ubaa8\ub450 \ub2eb\ud78c \ub2e4\uac01\ud615\uc774\uace0, \uad50\ucc28\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\uc885\uc774\ub294 \ubaa8\ub450 \uc9c1\uc0ac\uac01\ud615\uc774\uace0, x\ucd95\uacfc y\ucd95\uc5d0 \ud3c9\ud589\ud574\uc57c \ud55c\ub2e4. \uc11c\ub85c \uc811\ud558\ub294 \uc885\uc774\uc758 \uaf2d\uc9c0\uc810\uc740 \uc77c\uce58\ud574\uc57c \ud558\uace0, \uc885\uc774\ub97c \ud68c\uc804\ud560 \uc218\ub294 \uc5c6\ub2e4. \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c0\ub294 \ubaa8\ub4e0 \uc88c\ud45c\ub294 \uc815\uc218\uc774\uc9c0\ub9cc, \uc885\uc774\ub294 \uc815\uc218\uac00 \uc544\ub2cc \uc88c\ud45c\uc5d0 \ub193\uc744 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc9c0\ub3c4\ub294 \uc885\uc774\uc758 \uc678\uac01\uc120\uc5d0 \uc811\ud574\ub3c4 \ub41c\ub2e4. \uc18c\uc218\uc810 \uacc4\uc0b0\uc73c\ub85c \uc0dd\uae30\ub294 \uc624\ucc28\ub97c \ud53c\ud558\uae30 \uc704\ud574, \uc9c0\ub3c4\uac00 \uc885\uc774\uc758 \ubc14\uae65\uc73c\ub85c 10<sup>-6<\/sup> \uae4c\uc9c0 \ub118\uc5b4\uac00\ub3c4 \uc815\ub2f5\uc740 \uac19\ub2e4.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc9c0\ub3c4\uc758 \uaf2d\uc9c0\uc810\uc758 \uc218 n (3 &le; n &le; 50), \uc885\uc774\uc758 \ud06c\uae30 x<sub>s<\/sub>, y<sub>s<\/sub> (1 &le; x<sub>s<\/sub>, y<sub>s<\/sub> &le; 100)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c n\uac1c \uc904\uc5d0\ub294 \uc9c0\ub3c4\uc758 \uaf2d\uc9c0\uc810\uc744 \ub098\ud0c0\ub0b4\ub294 \ub450 \uc815\uc218 x\uc640 y\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (0 &le; x &le; 10x<sub>s<\/sub>, 0 &le; y &le; 10y<sub>s<\/sub>) \uaf2d\uc9c0\uc810\uc740 \uc2dc\uacc4\ubc29\ud5a5 \ub610\ub294 \ubc18\uc2dc\uacc4\ubc29\ud5a5\uc73c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc9c0\ub3c4\ub97c \uc778\uc1c4\ud558\uae30 \uc704\ud574 \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":"8883","problem_lang":"1","title":"Map Tiles","description":"<p>Publishing maps is not an easy task. First you need some appropriate transformation to display the earth&rsquo;s spherical shape in a two-dimensional plane. Then another issue arises &ndash; most high-quality maps are too large to be printed on a single page of paper. To cope with that, map publishers often split maps into several rectangular tiles, and print each tile on one page. In this problem, you will examine this &ldquo;tiling&rdquo; process.<\/p>\r\n\r\n<p>The International Cartographic Publishing Company (ICPC) needs to cut their printing costs by minimizing the number of tiles used for their maps. Even with a \ufb01xed tile size (determined by the page size) and map scale, you can still optimize the situation by adjusting the tile grid.<\/p>\r\n\r\n<p>The left side of Figure G.1 shows 14 map tiles covering a region. The right side shows how you can cover the same region with only 10 tiles, without changing the tile sizes or orientation.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/tile(2).png\" style=\"height:220px; width:395px\" \/><\/p>\r\n\r\n<p>Figure G.1: Two possible ways of tiling Texas.<\/p>\r\n\r\n<p>Your task is to help the ICPC \ufb01nd the minimum number of tiles needed to cover a given region. For simplicity, the region will be given as a closed polygon that does not intersect itself.<\/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. Also note that although all input coordinates are integers, tiles may be located at non-integer coordinates.<\/p>\r\n\r\n<p>The polygon may touch the edges of marginal lines (as in Sample Input 2). However, to avoid floating point issues, you may assume the optimal answer will not change even if the polygon is allowed to go outside the map tiles by a distance of 10<sup>-6<\/sup>.<\/p>\r\n","input":"<p>The input consists of a single test case. The \ufb01rst line of a test case contains three integers: n, x<sub>s<\/sub>, and y<sub>s<\/sub>. The number of polygon vertices is n (3 &le; n &le; 50), and x<sub>s<\/sub> and y<sub>s<\/sub> (1 &le; x<sub>s<\/sub>, y<sub>s<\/sub> &le; 100) are the dimensions of each tile. Each of the next n lines contains two integers x and y (0 &le; x &le; 10x<sub>s<\/sub>, 0 &le; y &le; 10y<sub>s<\/sub>), specifying the vertices of the polygon representing the region (in either clockwise or counter-clockwise order).<\/p>\r\n","output":"<p>Display the minimal number of tiles necessary to cover the whole interior of the polygon.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ACM-ICPC > World Finals > 2013 World Finals G번