시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
10 초 128 MB 816 272 147 25.835%

문제

명우는 픽업 게임을 하려고 한다. 규칙은 다음과 같다.

  1. 아래 그림과 같은 가로, 세로 선이 여러 개 있다.
  2. 선분의 교점을 클릭하면 교점을 이루는 두 선분을 집어갈 수 있다. (집어가면 두 선분은 사라진다)
  3. 모든 선분은 무게가 있다.
  4. 무게가 a와 b인 선분을 집어갈 때, 얻는 점수는 a × b이다.

게임의 첫 번째 목표는 최대한 많은 선분을 집어가는 것이다. 두 번째 목표는 최대한 많은 점수를 얻는 것이다. 즉, 선분을 많이 집어가는 방법이 여러 가지라면, 점수를 최대로 하는 방법으로 집어가야 한다.

게임의 정보가 주어졌을 때, 집을 수 있는 선분의 최대 개수와, 최대 점수를 구하는 프로그램을 작성하시오.

입력

첫째 줄에 테스트 케이스의 개수 T가 주어진다. 각 테스트 케이스의 첫째 줄에는 가로 선의 수 n과 세로 선의 수 m이 주어진다. (1 ≤ n,m ≤ 200) 다음 n개 줄에는 각 가로 선의 정보 x,y,x',y',w가 주어진다. (x,y)와 (x',y')는 선분의 양 끝 점을 나타내고, w는 그 선분의 무게이다. (y = y') 다음 m개 줄에는 세로 선의 정보가 가로 선의 정보와 같은 형식으로 주어진다. 모든 좌표는 양수이고 100,000보다 작거나 같다. 또한, 무게도 양수이며 20보다 작거나 같다. 모든 선분 쌍은 최대 한 개의 점에서 만나며, 끝 점에서 만나는 경우는 없다.

출력

각 테스트 케이스마다 두 정수를 출력한다. 첫 정수는 집을 수 있는 선분의 쌍의 개수의 최댓값이고, 두 번째는 그 쌍의 개수만큼을 집어가면서 얻을 수 있는 최대 점수이다.

예제 입력 1

2
2 2
1 2 4 2 1
1 3 4 3 2
2 1 2 4 3
3 1 3 4 4
2 2
1 2 5 2 3
7 2 6 2 3
2 3 2 1 2
3 1 3 3 1

예제 출력 1

2 11
1 6
[{"problem_id":"8992","problem_lang":"0","title":"\uc9d1\uae30 \uac8c\uc784","description":"<p>\uba85\uc6b0\ub294 \ud53d\uc5c5 \uac8c\uc784\uc744 \ud558\ub824\uace0 \ud55c\ub2e4. \uaddc\uce59\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\r\n\r\n<ol>\r\n\t<li>\uc544\ub798 \uadf8\ub9bc\uacfc \uac19\uc740 \uac00\ub85c, \uc138\ub85c \uc120\uc774 \uc5ec\ub7ec \uac1c \uc788\ub2e4.<\/li>\r\n\t<li>\uc120\ubd84\uc758 \uad50\uc810\uc744 \ud074\ub9ad\ud558\uba74 \uad50\uc810\uc744 \uc774\ub8e8\ub294 \ub450 \uc120\ubd84\uc744 \uc9d1\uc5b4\uac08 \uc218 \uc788\ub2e4. (\uc9d1\uc5b4\uac00\uba74 \ub450 \uc120\ubd84\uc740 \uc0ac\ub77c\uc9c4\ub2e4)<\/li>\r\n\t<li>\ubaa8\ub4e0 \uc120\ubd84\uc740 \ubb34\uac8c\uac00 \uc788\ub2e4.<\/li>\r\n\t<li>\ubb34\uac8c\uac00 a\uc640 b\uc778 \uc120\ubd84\uc744 \uc9d1\uc5b4\uac08 \ub54c, \uc5bb\ub294 \uc810\uc218\ub294 a &times; b\uc774\ub2e4.<\/li>\r\n<\/ol>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/lineseg.png\" style=\"height:213px; width:221px\" \/><\/p>\r\n\r\n<p>\uac8c\uc784\uc758 \uccab \ubc88\uc9f8 \ubaa9\ud45c\ub294 \ucd5c\ub300\ud55c \ub9ce\uc740 \uc120\ubd84\uc744 \uc9d1\uc5b4\uac00\ub294 \uac83\uc774\ub2e4. \ub450 \ubc88\uc9f8 \ubaa9\ud45c\ub294 \ucd5c\ub300\ud55c \ub9ce\uc740 \uc810\uc218\ub97c \uc5bb\ub294 \uac83\uc774\ub2e4. \uc989, \uc120\ubd84\uc744 \ub9ce\uc774 \uc9d1\uc5b4\uac00\ub294 \ubc29\ubc95\uc774 \uc5ec\ub7ec \uac00\uc9c0\ub77c\uba74, \uc810\uc218\ub97c \ucd5c\ub300\ub85c \ud558\ub294 \ubc29\ubc95\uc73c\ub85c \uc9d1\uc5b4\uac00\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uac8c\uc784\uc758 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc9d1\uc744 \uc218 \uc788\ub294 \uc120\ubd84\uc758 \ucd5c\ub300 \uac1c\uc218\uc640, \ucd5c\ub300 \uc810\uc218\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 \uac00\ub85c \uc120\uc758 \uc218 n\uacfc \uc138\ub85c \uc120\uc758 \uc218 m\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; n,m &le; 200) \ub2e4\uc74c n\uac1c \uc904\uc5d0\ub294 \uac01 \uac00\ub85c \uc120\uc758 \uc815\ubcf4 x,y,x&#39;,y&#39;,w\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (x,y)\uc640 (x&#39;,y&#39;)\ub294 \uc120\ubd84\uc758 \uc591 \ub05d \uc810\uc744 \ub098\ud0c0\ub0b4\uace0, w\ub294 \uadf8 \uc120\ubd84\uc758 \ubb34\uac8c\uc774\ub2e4. (y = y&#39;) \ub2e4\uc74c m\uac1c \uc904\uc5d0\ub294 \uc138\ub85c \uc120\uc758 \uc815\ubcf4\uac00 \uac00\ub85c \uc120\uc758 \uc815\ubcf4\uc640 \uac19\uc740 \ud615\uc2dd\uc73c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \ubaa8\ub4e0 \uc88c\ud45c\ub294 \uc591\uc218\uc774\uace0&nbsp;100,000\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\ub2e4. \ub610\ud55c, \ubb34\uac8c\ub3c4 \uc591\uc218\uc774\uba70&nbsp;20\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\ub2e4. \ubaa8\ub4e0 \uc120\ubd84 \uc30d\uc740 \ucd5c\ub300 \ud55c \uac1c\uc758 \uc810\uc5d0\uc11c \ub9cc\ub098\uba70, \ub05d \uc810\uc5d0\uc11c \ub9cc\ub098\ub294 \uacbd\uc6b0\ub294 \uc5c6\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 \ub450 \uc815\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4. \uccab \uc815\uc218\ub294 \uc9d1\uc744 \uc218 \uc788\ub294 \uc120\ubd84\uc758 \uc30d\uc758 \uac1c\uc218\uc758 \ucd5c\ub313\uac12\uc774\uace0, \ub450 \ubc88\uc9f8\ub294 \uadf8 \uc30d\uc758 \uac1c\uc218\ub9cc\ud07c\uc744 \uc9d1\uc5b4\uac00\uba74\uc11c \uc5bb\uc744 \uc218 \uc788\ub294 \ucd5c\ub300 \uc810\uc218\uc774\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"8992","problem_lang":"1","title":"Pickup Game","description":"<p>You are playing a computer game called the &quot;Pickup.&quot; The rules are as follows:&nbsp;<\/p>\r\n\r\n<ol>\r\n\t<li>There are a number of horizontal and vertical line segments. (See the figure below.)&nbsp;<\/li>\r\n\t<li>You can &quot;Pickup&quot; a pair of line segments by clicking on the crossing made by the pair. (The pair disappears from screen when you do this.)&nbsp;<\/li>\r\n\t<li>Each line segment is given a weight.&nbsp;<\/li>\r\n\t<li>When you pick up a pair with weights a and b, you are given a score of a &times; b.<\/li>\r\n<\/ol>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/lineseg.png\" style=\"height:213px; width:221px\" \/><\/p>\r\n\r\n<p>Figure 1. An Example Screen&nbsp;<\/p>\r\n\r\n<p>The first goal is to pick up the most line segments. The second goal is to maximize the total score. That is, if there are more than one way of picking up the most line segments, then you have to find the one with the largest possible score.&nbsp;<\/p>\r\n\r\n<p>Write a program, given the specification of an instance of the game, which computes the maximum possible number of line segments that can be picked up and the maximum possible score.&nbsp;<\/p>\r\n","input":"<p>Your program is to read from standard input. The input consists of T test cases. The number of test cases T is given in the first line of the input. Each test case starts with integers n and m, the number of horizontal and vertical line segments, respectively, where 1 &le; n, m &le; 200. Each of the following n lines contains five integers x,y,x&#39;,y&#39;,w, representing the two endpoints (note, y = y&prime;) and the weight of each horizontal line segment. Also each of the following m lines contains an analogous information for each vertical line segment. All coordinate values are positive and are less than or equal to 100,000. The weights are also positive and are less than or equal to 20. Any pair of line segments may share at most one point which is never an endpoint of the line segments.&nbsp;<\/p>\r\n","output":"<p>Your program is to write to standard output. Print exactly one line containing two integers for each test case. You should output the maximum possible number of line segment pairs that can be picked up, followed by maximum possible score while picking up the most pairs of line segments.&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]