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문제

병찬이는 친구 공찬이를 위해 맛있는 피자를 시켰다. 하지만 공찬이는 올리브를 싫어해서 피자를 잘라서 먹으려고 한다.

병찬이가 갖고 온 피자는 볼록다각형 모양을 하고 있으며, 올리브는 피자 안에 박혀있다. 공찬이는 피자를 보다 편하게 자르기 위해 인접하지 않은 두 꼭짓점을 선택하여 그 두 꼭짓점을 잇는 직선을 따라 피자를 자른다. 공찬이는 잘린 피자의 두 조각 중 올리브가 없는 쪽을 선택해서 먹을 것이다. 다만, 공찬이가 자르는 직선 위에 올리브가 있는 경우 올리브가 두 갈래로 잘리므로 두 조각 모두 먹지 못한다.

이 그림은 첫 번째 예제의 피자 모양이다. 공찬이가 자른 흔적이 점선으로 남아있다.

병찬이는 피자를 많이 먹지 않기 때문에 공찬이는 자신이 먹을 부분이 최대한 크게 피자를 자르려고 한다. 공찬이를 도와 얼마나 피자를 크게 자를 수 있는지 구하는 프로그램을 작성하여라.

입력

첫 번째 줄에는 피자의 꼭짓점의 수 N이 주어진다.

두 번째 줄부터 N개의 줄에는 피자의 각 꼭짓점의 좌표 Xi, Yi가 주어진다. 피자의 꼭짓점은 시계 반대 방향으로 주어진다. 피자에서 만들어지는 N개의 각들은 전부 180도보다 작다.

N+2번째 줄에는 올리브의 수 M이 주어진다.

N+3번째 줄부터 M개의 줄에는 올리브의 좌표 Xi, Yi가 주어진다. 올리브가 피자의 변 위에 있거나 피자 밖에 있는 경우는 존재하지 않으며, 올리브는 매우 작아서 점으로 간주해도 상관없다.

출력

만약 공찬이가 피자를 어떻게 자르더라도 두 조각 모두 올리브가 있는 경우 0을 출력한다.

그렇지 않은 경우 공찬이가 먹을 수 있는 피자의 최대 넓이를 2로 곱한 값을 출력한다. 잘 생각해보면, 답은 항상 정수임을 알 수 있다.

제한

모든 좌표는 [-109, 109] 범위에 있다.

서브태스크

번호배점제한
112

4 ≤ N ≤ 300, 1 ≤ M ≤ 300

239

4 ≤ N ≤ 3 000, 1 ≤ M ≤ 3 000

349

4 ≤ N ≤ 300 000, 1 ≤ M ≤ 300 000

예제 입력 1

5
0 1
3 0
4 2
2 3
0 3
3
2 1
3 1
3 2

예제 출력 1

4

예제 입력 2

6
-3 3
-3 -4
-2 -5
2 -5
3 -4
3 3
7
1 0
0 -1
0 -3
2 0
0 0
0 2
-1 0

예제 출력 2

10

예제 입력 3

6
0 3
-1 2
-1 -2
0 -3
1 -2
1 2
1
0 0

예제 출력 3

4

힌트

예제 2 설명: 공찬이는 피자의 2번 점과 5번 점을 잇는 직선을 따라 피자를 자르면 된다.

예제 3 설명: 공찬이는 피자의 1번 점과 3번 점을 잇는 직선을 따라 피자를 자르면 된다.

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line-height:20.8px; opacity:0.9; text-align:center; width:289px\" \/><\/p>\r\n\r\n<p style=\"text-align:center\">\uc774 \uadf8\ub9bc\uc740 \uccab \ubc88\uc9f8 \uc608\uc81c\uc758 \ud53c\uc790 \ubaa8\uc591\uc774\ub2e4. \uacf5\ucc2c\uc774\uac00 \uc790\ub978 \ud754\uc801\uc774 \uc810\uc120\uc73c\ub85c \ub0a8\uc544\uc788\ub2e4.<\/p>\r\n\r\n<p>\ubcd1\ucc2c\uc774\ub294 \ud53c\uc790\ub97c \ub9ce\uc774 \uba39\uc9c0 \uc54a\uae30 \ub54c\ubb38\uc5d0 \uacf5\ucc2c\uc774\ub294 \uc790\uc2e0\uc774 \uba39\uc744 \ubd80\ubd84\uc774 \ucd5c\ub300\ud55c \ud06c\uac8c \ud53c\uc790\ub97c \uc790\ub974\ub824\uace0 \ud55c\ub2e4. \uacf5\ucc2c\uc774\ub97c \ub3c4\uc640 \uc5bc\ub9c8\ub098 \ud53c\uc790\ub97c \ud06c\uac8c \uc790\ub97c \uc218 \uc788\ub294\uc9c0 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc5ec\ub77c.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0\ub294 \ud53c\uc790\uc758 \uaf2d\uc9d3\uc810\uc758 \uc218 N\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\ubd80\ud130 N\uac1c\uc758 \uc904\uc5d0\ub294 \ud53c\uc790\uc758 \uac01 \uaf2d\uc9d3\uc810\uc758 \uc88c\ud45c X<sub>i<\/sub>, Y<sub>i<\/sub>\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ud53c\uc790\uc758 \uaf2d\uc9d3\uc810\uc740 \uc2dc\uacc4 \ubc18\ub300 \ubc29\ud5a5\uc73c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \ud53c\uc790\uc5d0\uc11c \ub9cc\ub4e4\uc5b4\uc9c0\ub294 N\uac1c\uc758 \uac01\ub4e4\uc740 \uc804\ubd80 180\ub3c4\ubcf4\ub2e4 \uc791\ub2e4.<\/p>\r\n\r\n<p>N+2\ubc88\uc9f8 \uc904\uc5d0\ub294 \uc62c\ub9ac\ube0c\uc758 \uc218 M\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>N+3\ubc88\uc9f8 \uc904\ubd80\ud130 M\uac1c\uc758 \uc904\uc5d0\ub294 \uc62c\ub9ac\ube0c\uc758 \uc88c\ud45c Xi, Yi\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc62c\ub9ac\ube0c\uac00 \ud53c\uc790\uc758 \ubcc0 \uc704\uc5d0 \uc788\uac70\ub098 \ud53c\uc790 \ubc16\uc5d0 \uc788\ub294 \uacbd\uc6b0\ub294 \uc874\uc7ac\ud558\uc9c0 \uc54a\uc73c\uba70, \uc62c\ub9ac\ube0c\ub294 \ub9e4\uc6b0 \uc791\uc544\uc11c \uc810\uc73c\ub85c \uac04\uc8fc\ud574\ub3c4 \uc0c1\uad00\uc5c6\ub2e4.<\/p>\r\n","output":"<p>\ub9cc\uc57d \uacf5\ucc2c\uc774\uac00 \ud53c\uc790\ub97c \uc5b4\ub5bb\uac8c \uc790\ub974\ub354\ub77c\ub3c4 \ub450 \uc870\uac01 \ubaa8\ub450 \uc62c\ub9ac\ube0c\uac00 \uc788\ub294 \uacbd\uc6b0 0\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uadf8\ub807\uc9c0 \uc54a\uc740 \uacbd\uc6b0 \uacf5\ucc2c\uc774\uac00 \uba39\uc744 \uc218 \uc788\ub294 \ud53c\uc790\uc758 \ucd5c\ub300 \ub113\uc774\ub97c 2\ub85c \uacf1\ud55c \uac12\uc744 \ucd9c\ub825\ud55c\ub2e4. \uc798 \uc0dd\uac01\ud574\ubcf4\uba74, \ub2f5\uc740 \ud56d\uc0c1 \uc815\uc218\uc784\uc744 \uc54c \uc218 \uc788\ub2e4.<\/p>\r\n","hint":"<p>\uc608\uc81c 2 \uc124\uba85: \uacf5\ucc2c\uc774\ub294 \ud53c\uc790\uc758 2\ubc88 \uc810\uacfc 5\ubc88 \uc810\uc744 \uc787\ub294 \uc9c1\uc120\uc744 \ub530\ub77c \ud53c\uc790\ub97c \uc790\ub974\uba74 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc608\uc81c 3 \uc124\uba85: \uacf5\ucc2c\uc774\ub294 \ud53c\uc790\uc758 1\ubc88 \uc810\uacfc 3\ubc88 \uc810\uc744 \uc787\ub294 \uc9c1\uc120\uc744 \ub530\ub77c \ud53c\uc790\ub97c \uc790\ub974\uba74 \ub41c\ub2e4.<\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"Korean","limit":"<p>\ubaa8\ub4e0 \uc88c\ud45c\ub294 [-10<sup>9<\/sup>, 10<sup>9<\/sup>] \ubc94\uc704\uc5d0 \uc788\ub2e4.<\/p>\r\n","subtask1":"<p>4 &le;&nbsp;N &le; 300, 1 &le;&nbsp;M &le; 300<\/p>\r\n","subtask2":"<p>4 &le; N &le; 3 000, 1 &le; M &le; 3 000<\/p>\r\n","subtask3":"<p>4 &le; N &le; 300 000, 1 &le; M &le; 300 000<\/p>\r\n"},{"problem_id":"10756","problem_lang":"1","title":"SIR","description":"<p>Kre&scaron;o has bought some delicious cheese with peppers, but Stjepan doesn&rsquo;t really like peppers so he&rsquo;s trying to cut a piece that doesn&rsquo;t contain any peppers.<\/p>\r\n\r\n<p>Kre&scaron;o&rsquo;s cheese has the shape of a convex polygon, and each pepper is one point on the inside of the polygon. Stjepan cuts the cheese exactly once in such a way that he chooses two vertices of the polygon that are not adjacent and cuts along the line segment connecting them. Stjepan then takes the freshly cut part without any peppers (on the inside nor on the edges).<\/p>\r\n\r\n<p style=\"text-align:center\"><img alt=\"\" src=\"\/upload\/images3\/sir.png\" style=\"height:246px; width:289px\" \/><\/p>\r\n\r\n<p style=\"text-align:center\">The image corresponds to the first sample test. The dotted line marks Stjepan&rsquo;s cut.<\/p>\r\n\r\n<p>Write a programme that will determine whether Stjepan can cut a piece of cheese without any peppers. If he can, determine the maximum possible area of the piece of cheese without peppers that Stjepan can cut.<\/p>\r\n","input":"<p>The first line of input contains the integer N &ndash; the number of vertices of the convex polygon representing the cheese.<\/p>\r\n\r\n<p>Each of the following N lines contains two integers X<sub>i<\/sub> and Y<sub>i<\/sub> &ndash; coordinates of the i<sup>th<\/sup> polygon vertex. The following line contains the integer M &ndash; the number of peppers. Each of the following M lines contains two integers X<sub>i<\/sub> and Y<sub>i<\/sub> &ndash; coordinates of the i<sup>th<\/sup> peppers.<\/p>\r\n\r\n<p>The polygon vertices are given in counter-clockwise order and form a convex polygon. None two adjacent edges are parallel.<\/p>\r\n\r\n<p>All peppers are located in different coordinates in the inside of the polygon (they will not be located on the edge or outside of the polygon).<\/p>\r\n","output":"<p>The first and only line of output must contain an integer &ndash; twice the maximum possible area (the double area is always going to be an integer).<\/p>\r\n\r\n<p>If it isn&rsquo;t possible to cut a piece of cheese without peppers in one move, output 0.<\/p>\r\n","hint":"<p>Clarification of the second example: Stjepan cuts from vertex 2 to vertex 5.<\/p>\r\n\r\n<p>Clarification of the third example: Stjepan cuts from vertex 1 to vertex 3.<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"English","limit":"<p>In all subtasks, the coordinates will be from the interval [-10<sup>9<\/sup>, 10<sup>9<\/sup>].<\/p>\r\n","subtask1":"<p>4 &le;&nbsp;N &le; 300, 1 &le;&nbsp;M &le; 300<\/p>\r\n","subtask2":"<p>4 &le; N &le; 3 000, 1 &le; M &le; 3 000<\/p>\r\n","subtask3":"<p>4 &le; N &le; 300 000, 1 &le; M &le; 300 000<\/p>\r\n"}]

출처

Olympiad > Croatian Highschool Competitions in Informatics > 2015 > Croatian Olympiad in Informatics 2015 4번

채점 및 기타 정보

  • 예제는 채점하지 않는다.