시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 21 8 6 46.154%

문제

상근이의 방의 한쪽 벽에는 못이 N개 박혀 있다. 아침에 일찍 일어나서 이 벽을 바라보며 하루를 어떻게 살 것인가를 생각하던 중에 상근이는 이 벽은 2차원 평면이고, 못은 그 평면 위의 점과 같다는 생각을 했다. 서로 다른 두 못은 같은 x좌표나 y좌표를 갖지 않는다.

마침 바닥에 고무줄이 하나 떨어져 있엇다. 상근이는 고무줄 안에 모든 못이 포함되도록 못에 고무줄을 걸어 놓았다. 이 고무줄은 매우 비싼 고무줄이기 때문에 끊어지지 않는다.

상근이는 벽에 있는 못의 개수가 세 개 이상인 동안에 아래와 같은 과정을 거쳐 벽에 있는 못을 빼려고 한다.

  1. 고무줄이 만드는 다각형의 면적을 적는다.
  2. 가장 왼쪽, 오른쪽, 위, 아래에 있는 못 중 하나를 고른다.
  3. 2번에서 고른 못을 벽에서 제거한다. 그럼 고무줄은 남은 못을 모두 감싸게 된다.

상근이가 2번 단계에서 고른 못이 어떤 못인지 주어졌을 때, 1번 단계에서 적는 면적을 모두 구하는 프로그램을 작성하시오.

입력

첫째 줄에 못의 개수 N이 주어진다. (3 ≤ N ≤ 300,000)

다음 N개 줄에는 못의 좌표가 주어진다. 모든 좌표는 1과 1,000,000,000 사이이며, 서로 다른 두 못이 같은 x좌표나 y좌표를 갖는 경우는 없다.

마지막 줄에는 'L', 'R',' U', 'D'로 이루어진 N-2개의 문자열이 주어진다. 이 문자열은 상근이가 2번단계에서 고른 못의 정보이며, 다음과 같은 의미를 갖는다.

  • 'L': 가장 왼쪽 못 (가장 작은 x좌표)
  • 'R': 가장 오른쪽 못 (가장 큰 x좌표)
  • 'U': 가장 위쪽 못 (가장 큰 y좌표)
  • 'D': 가장 아래쪽 못 (가장 작은 y좌표)

출력

상근이가 1번 단계에서 구하는 면적을 순서대로 한 줄에 하나씩 출력한다. 출력은 소수점 첫째 자리까지 출력한다. 

예제 입력 1

8
1 6
2 4
3 1
4 2
5 7
6 5
7 9
8 3
URDLUU

예제 출력 1

34.0
24.0
16.5
14.0
9.5
5.0

힌트

[{"problem_id":"2964","problem_lang":"0","title":"\ubcbd\uacfc \ubabb","description":"<p>\uc0c1\uadfc\uc774\uc758 \ubc29\uc758 \ud55c\ucabd \ubcbd\uc5d0\ub294 \ubabb\uc774 N\uac1c \ubc15\ud600 \uc788\ub2e4. \uc544\uce68\uc5d0 \uc77c\ucc0d \uc77c\uc5b4\ub098\uc11c \uc774 \ubcbd\uc744 \ubc14\ub77c\ubcf4\uba70 \ud558\ub8e8\ub97c \uc5b4\ub5bb\uac8c \uc0b4 \uac83\uc778\uac00\ub97c \uc0dd\uac01\ud558\ub358 \uc911\uc5d0 \uc0c1\uadfc\uc774\ub294 \uc774 \ubcbd\uc740 2\ucc28\uc6d0 \ud3c9\uba74\uc774\uace0, \ubabb\uc740 \uadf8 \ud3c9\uba74 \uc704\uc758 \uc810\uacfc \uac19\ub2e4\ub294 \uc0dd\uac01\uc744 \ud588\ub2e4. \uc11c\ub85c \ub2e4\ub978 \ub450 \ubabb\uc740 \uac19\uc740 x\uc88c\ud45c\ub098 y\uc88c\ud45c\ub97c \uac16\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\ub9c8\uce68 \ubc14\ub2e5\uc5d0 \uace0\ubb34\uc904\uc774 \ud558\ub098 \ub5a8\uc5b4\uc838 \uc788\uc5c7\ub2e4. \uc0c1\uadfc\uc774\ub294 \uace0\ubb34\uc904 \uc548\uc5d0 \ubaa8\ub4e0 \ubabb\uc774 \ud3ec\ud568\ub418\ub3c4\ub85d \ubabb\uc5d0 \uace0\ubb34\uc904\uc744 \uac78\uc5b4 \ub193\uc558\ub2e4. \uc774 \uace0\ubb34\uc904\uc740 \ub9e4\uc6b0 \ube44\uc2fc \uace0\ubb34\uc904\uc774\uae30 \ub54c\ubb38\uc5d0 \ub04a\uc5b4\uc9c0\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\uc0c1\uadfc\uc774\ub294 \ubcbd\uc5d0 \uc788\ub294 \ubabb\uc758 \uac1c\uc218\uac00 \uc138 \uac1c \uc774\uc0c1\uc778 \ub3d9\uc548\uc5d0 \uc544\ub798\uc640 \uac19\uc740 \uacfc\uc815\uc744 \uac70\uccd0 \ubcbd\uc5d0 \uc788\ub294 \ubabb\uc744 \ube7c\ub824\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<ol>\r\n\t<li>\uace0\ubb34\uc904\uc774 \ub9cc\ub4dc\ub294 \ub2e4\uac01\ud615\uc758 \uba74\uc801\uc744 \uc801\ub294\ub2e4.<\/li>\r\n\t<li>\uac00\uc7a5 \uc67c\ucabd, \uc624\ub978\ucabd, \uc704, \uc544\ub798\uc5d0 \uc788\ub294 \ubabb \uc911 \ud558\ub098\ub97c \uace0\ub978\ub2e4.<\/li>\r\n\t<li>2\ubc88\uc5d0\uc11c \uace0\ub978 \ubabb\uc744 \ubcbd\uc5d0\uc11c \uc81c\uac70\ud55c\ub2e4. \uadf8\ub7fc \uace0\ubb34\uc904\uc740 \ub0a8\uc740 \ubabb\uc744 \ubaa8\ub450 \uac10\uc2f8\uac8c \ub41c\ub2e4.<\/li>\r\n<\/ol>\r\n\r\n<p>\uc0c1\uadfc\uc774\uac00 2\ubc88 \ub2e8\uacc4\uc5d0\uc11c \uace0\ub978 \ubabb\uc774 \uc5b4\ub5a4 \ubabb\uc778\uc9c0 \uc8fc\uc5b4\uc84c\uc744 \ub54c, 1\ubc88 \ub2e8\uacc4\uc5d0\uc11c \uc801\ub294 \uba74\uc801\uc744 \ubaa8\ub450 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ubabb\uc758 \uac1c\uc218 N\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (3 &le; N &le; 300,000)<\/p>\r\n\r\n<p>\ub2e4\uc74c N\uac1c \uc904\uc5d0\ub294 \ubabb\uc758 \uc88c\ud45c\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ubaa8\ub4e0 \uc88c\ud45c\ub294 1\uacfc 1,000,000,000 \uc0ac\uc774\uc774\uba70, \uc11c\ub85c \ub2e4\ub978 \ub450 \ubabb\uc774 \uac19\uc740 x\uc88c\ud45c\ub098 y\uc88c\ud45c\ub97c \uac16\ub294 \uacbd\uc6b0\ub294 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 &#39;L&#39;, &#39;R&#39;,&#39; U&#39;, &#39;D&#39;\ub85c \uc774\ub8e8\uc5b4\uc9c4 N-2\uac1c\uc758 \ubb38\uc790\uc5f4\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774 \ubb38\uc790\uc5f4\uc740 \uc0c1\uadfc\uc774\uac00 2\ubc88\ub2e8\uacc4\uc5d0\uc11c \uace0\ub978 \ubabb\uc758 \uc815\ubcf4\uc774\uba70, \ub2e4\uc74c\uacfc \uac19\uc740 \uc758\ubbf8\ub97c \uac16\ub294\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>&#39;L&#39;: \uac00\uc7a5 \uc67c\ucabd \ubabb (\uac00\uc7a5 \uc791\uc740 x\uc88c\ud45c)<\/li>\r\n\t<li>&#39;R&#39;: \uac00\uc7a5 \uc624\ub978\ucabd \ubabb (\uac00\uc7a5 \ud070 x\uc88c\ud45c)<\/li>\r\n\t<li>&#39;U&#39;: \uac00\uc7a5 \uc704\ucabd \ubabb (\uac00\uc7a5 \ud070 y\uc88c\ud45c)<\/li>\r\n\t<li>&#39;D&#39;: \uac00\uc7a5 \uc544\ub798\ucabd \ubabb (\uac00\uc7a5 \uc791\uc740 y\uc88c\ud45c)<\/li>\r\n<\/ul>\r\n","output":"<p>\uc0c1\uadfc\uc774\uac00 1\ubc88 \ub2e8\uacc4\uc5d0\uc11c \uad6c\ud558\ub294 \uba74\uc801\uc744 \uc21c\uc11c\ub300\ub85c \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \ucd9c\ub825\ud55c\ub2e4. \ucd9c\ub825\uc740 \uc18c\uc218\uc810 \uccab\uc9f8 \uc790\ub9ac\uae4c\uc9c0 \ucd9c\ub825\ud55c\ub2e4.&nbsp;<\/p>\r\n","hint":"<p><img alt=\"\" src=\"\/upload\/images\/nail.png\" style=\"height:412px; width:624px\" \/><\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2964","problem_lang":"1","title":"CAVLI","description":"<p>Mirko found a wooden board and N nails in his attic. Mirko hammered the nails into the board as fast as possible. The board can be modeled by a coordinate plane and the nails as points in it. No two nails have the same x or the same y coordinate.&nbsp;<\/p>\r\n\r\n<p>In order to keep having fun, Mirko stole his sister&#39;s elastic hair band, spread it over all nails and then let go. The elastic, naturally, tightened around the nails.&nbsp;<\/p>\r\n\r\n<p>Mirko then repeats these steps while there are at least three nails in the board:&nbsp;<\/p>\r\n\r\n<ol>\r\n\t<li>Write down the area of the shape enclosed by the hair band.&nbsp;<\/li>\r\n\t<li>Picks the leftmost, rightmost, topmost or bottommost nail in the board.&nbsp;<\/li>\r\n\t<li>Remove the chosen nail from the board; the elastic tightens again around the remaining nails.&nbsp;<\/li>\r\n<\/ol>\r\n\r\n<p>Write a program that calculates the numbers written in step 1 of each iteration, if we know the nail Mirko picks in step 2 of each iteration.<\/p>\r\n","input":"<p>The first line contains the integer N (3 &le; N &le; 300000), the number of nails.&nbsp;<\/p>\r\n\r\n<p>Each of the following N lines contains two integers separated by a space, the coordinates of a nail. All coordinates will be between 1 and 1000000000. No two nails will share the same x or y coordinate.&nbsp;<\/p>\r\n\r\n<p>The next line contains N-2 letters &#39;L&#39;, &#39;R&#39;, &#39;U&#39; or &#39;D&#39;. The letters represent the nails Mirko picked in order:&nbsp;<\/p>\r\n\r\n<ul>\r\n\t<li>&#39;L&#39; for the leftmost nail (smallest x coordinate),&nbsp;<\/li>\r\n\t<li>&#39;R&#39; for the rightmost nail (largest x coordinate),&nbsp;<\/li>\r\n\t<li>&#39;U&#39; for the topmost nail (largest y coordinate),&nbsp;<\/li>\r\n\t<li>&#39;D&#39; for the bottommost nail (smallest y coordinate).<\/li>\r\n<\/ul>\r\n","output":"<p>Output N-2 numbers, each on a separate line. The numbers are, in order, the areas that Mirko wrote down. Output numbers with one digit after the decimal point.<\/p>\r\n","hint":"<p><img alt=\"\" src=\"\/upload\/images\/nail.png\" style=\"height:412px; opacity:0.9; width:624px\" \/><\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]