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문제

상근이는 2차원 평면 위에서 움직일 수 있는 거북이 로봇을 하나 가지고 있다. 거북이 로봇에게 내릴 수 있는 명령은 다음과 같이 네가지가 있다.

  1. F: 한 눈금 앞으로
  2. B: 한 눈금 뒤로
  3. L: 왼쪽으로 90도 회전
  4. R: 오른쪽으로 90도 회전

L과 R명령을 내렸을 때, 로봇은 이동하지 않고, 방향만 바꾼다. 명령을 나열한 것을 거북이 로봇의 컨트롤 프로그램이라고 한다.

상근이는 자신의 컨트롤 프로그램으로 거북이가 이동한 영역을 계산해보려고 한다. 거북이는 항상 x축과 y축에 평행한 방향으로만 이동한다. 거북이가 지나간 영역을 모두 포함할 수 있는 가장 작은 직사각형의 넓이를 구하는 프로그램을 작성하시오. 단, 직사각형의 모든 변은 x축이나 y축에 평행이어야 한다.

아래 그림에서 거북이는 가장 처음에 (0, 0)에 있고, 북쪽을 쳐다보고 있다. 컨트롤 프로그램이 FLFRFLBRBLB인 경우에 거북이는 아래와 같이 움직인다. 회색으로 빗금친 부분이 거북이가 지나간 영역을 모두 포함할 수 있는 가장 작은 직사각형이다. 넓이는 4가 된다.

거북이가 지나간 영역이 직사각형을 만들지 않는 경우도 있다. 예를 들어, FFLLFF인 경우에 거북이는 y축의 위로만 지나다닌다. 이 경우에 거북이가 지나간 영역을 모두 포함하는 직사각형은 선분이고, 선분은 한 변이 0인 직사각형으로 생각할 수 있다. 따라서, 선분의 경우에 넓이는 0이 된다.

입력

첫째 줄에 테스트 케이스의 개수 T가 주어진다. 각 테스트 케이스는 한 줄로 이루어져 있고, 컨트롤 프로그램이 주어진다. 프로그램은 항상 문제의 설명에 나와있는 네가지 명령으로만 이루어져 있고, 길이는 500을 넘지 않는다. 

출력

각 테스트 케이스에 대해서, 거북이가 이동한 영역을 모두 포함하는 가장 작은 직사각형의 넓이를 출력한다.

예제 입력 1

3
FFLF
FFRRFF
FFFBBBRFFFBBB

예제 출력 1

2
0
9
[{"problem_id":"8911","problem_lang":"0","title":"\uac70\ubd81\uc774","description":"<p><img alt=\"\" src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/upload\/images\/turtle2(1).png\" style=\"float:right; height:139px; width:183px\" \/>\uc0c1\uadfc\uc774\ub294 2\ucc28\uc6d0 \ud3c9\uba74 \uc704\uc5d0\uc11c \uc6c0\uc9c1\uc77c \uc218 \uc788\ub294 \uac70\ubd81\uc774 \ub85c\ubd07\uc744 \ud558\ub098 \uac00\uc9c0\uace0 \uc788\ub2e4. \uac70\ubd81\uc774 \ub85c\ubd07\uc5d0\uac8c \ub0b4\ub9b4 \uc218 \uc788\ub294 \uba85\ub839\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \ub124\uac00\uc9c0\uac00 \uc788\ub2e4.<\/p>\r\n\r\n<ol>\r\n\t<li>F: \ud55c \ub208\uae08 \uc55e\uc73c\ub85c<\/li>\r\n\t<li>B: \ud55c \ub208\uae08 \ub4a4\ub85c<\/li>\r\n\t<li>L: \uc67c\ucabd\uc73c\ub85c 90\ub3c4 \ud68c\uc804<\/li>\r\n\t<li>R: \uc624\ub978\ucabd\uc73c\ub85c 90\ub3c4 \ud68c\uc804<\/li>\r\n<\/ol>\r\n\r\n<p>L\uacfc R\uba85\ub839\uc744 \ub0b4\ub838\uc744 \ub54c, \ub85c\ubd07\uc740 \uc774\ub3d9\ud558\uc9c0 \uc54a\uace0, \ubc29\ud5a5\ub9cc \ubc14\uafbc\ub2e4. \uba85\ub839\uc744 \ub098\uc5f4\ud55c \uac83\uc744 \uac70\ubd81\uc774 \ub85c\ubd07\uc758 \ucee8\ud2b8\ub864 \ud504\ub85c\uadf8\ub7a8\uc774\ub77c\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc0c1\uadfc\uc774\ub294 \uc790\uc2e0\uc758 \ucee8\ud2b8\ub864 \ud504\ub85c\uadf8\ub7a8\uc73c\ub85c \uac70\ubd81\uc774\uac00 \uc774\ub3d9\ud55c \uc601\uc5ed\uc744 \uacc4\uc0b0\ud574\ubcf4\ub824\uace0 \ud55c\ub2e4. \uac70\ubd81\uc774\ub294 \ud56d\uc0c1 x\ucd95\uacfc y\ucd95\uc5d0 \ud3c9\ud589\ud55c \ubc29\ud5a5\uc73c\ub85c\ub9cc \uc774\ub3d9\ud55c\ub2e4. \uac70\ubd81\uc774\uac00 \uc9c0\ub098\uac04 \uc601\uc5ed\uc744 \ubaa8\ub450 \ud3ec\ud568\ud560 \uc218 \uc788\ub294 \uac00\uc7a5 \uc791\uc740 \uc9c1\uc0ac\uac01\ud615\uc758 \ub113\uc774\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.&nbsp;\ub2e8, \uc9c1\uc0ac\uac01\ud615\uc758 \ubaa8\ub4e0 \ubcc0\uc740 x\ucd95\uc774\ub098 y\ucd95\uc5d0 \ud3c9\ud589\uc774\uc5b4\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc544\ub798 \uadf8\ub9bc\uc5d0\uc11c \uac70\ubd81\uc774\ub294 \uac00\uc7a5 \ucc98\uc74c\uc5d0 (0, 0)\uc5d0 \uc788\uace0, \ubd81\ucabd\uc744 \uccd0\ub2e4\ubcf4\uace0 \uc788\ub2e4.&nbsp;\ucee8\ud2b8\ub864 \ud504\ub85c\uadf8\ub7a8\uc774 FLFRFLBRBLB\uc778 \uacbd\uc6b0\uc5d0 \uac70\ubd81\uc774\ub294 \uc544\ub798\uc640 \uac19\uc774 \uc6c0\uc9c1\uc778\ub2e4. \ud68c\uc0c9\uc73c\ub85c \ube57\uae08\uce5c \ubd80\ubd84\uc774 \uac70\ubd81\uc774\uac00 \uc9c0\ub098\uac04 \uc601\uc5ed\uc744 \ubaa8\ub450 \ud3ec\ud568\ud560 \uc218 \uc788\ub294 \uac00\uc7a5 \uc791\uc740 \uc9c1\uc0ac\uac01\ud615\uc774\ub2e4. \ub113\uc774\ub294 4\uac00 \ub41c\ub2e4.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/upload\/images\/turtle.png\" style=\"height:294px; width:304px\" \/><\/p>\r\n\r\n<p>\uac70\ubd81\uc774\uac00 \uc9c0\ub098\uac04 \uc601\uc5ed\uc774 \uc9c1\uc0ac\uac01\ud615\uc744 \ub9cc\ub4e4\uc9c0 \uc54a\ub294 \uacbd\uc6b0\ub3c4 \uc788\ub2e4. \uc608\ub97c \ub4e4\uc5b4, FFLLFF\uc778 \uacbd\uc6b0\uc5d0 \uac70\ubd81\uc774\ub294 y\ucd95\uc758 \uc704\ub85c\ub9cc \uc9c0\ub098\ub2e4\ub2cc\ub2e4. \uc774 \uacbd\uc6b0\uc5d0 \uac70\ubd81\uc774\uac00 \uc9c0\ub098\uac04 \uc601\uc5ed\uc744 \ubaa8\ub450 \ud3ec\ud568\ud558\ub294 \uc9c1\uc0ac\uac01\ud615\uc740 \uc120\ubd84\uc774\uace0, \uc120\ubd84\uc740 \ud55c \ubcc0\uc774 0\uc778 \uc9c1\uc0ac\uac01\ud615\uc73c\ub85c \uc0dd\uac01\ud560 \uc218 \uc788\ub2e4. \ub530\ub77c\uc11c, \uc120\ubd84\uc758 \uacbd\uc6b0\uc5d0 \ub113\uc774\ub294 0\uc774 \ub41c\ub2e4.<\/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\ub294 \ud55c \uc904\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uace0, \ucee8\ud2b8\ub864 \ud504\ub85c\uadf8\ub7a8\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ud504\ub85c\uadf8\ub7a8\uc740 \ud56d\uc0c1 \ubb38\uc81c\uc758 \uc124\uba85\uc5d0 \ub098\uc640\uc788\ub294 \ub124\uac00\uc9c0 \uba85\ub839\uc73c\ub85c\ub9cc \uc774\ub8e8\uc5b4\uc838 \uc788\uace0, \uae38\uc774\ub294 500\uc744 \ub118\uc9c0 \uc54a\ub294\ub2e4.&nbsp;<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574\uc11c, \uac70\ubd81\uc774\uac00 \uc774\ub3d9\ud55c \uc601\uc5ed\uc744 \ubaa8\ub450 \ud3ec\ud568\ud558\ub294 \uac00\uc7a5 \uc791\uc740 \uc9c1\uc0ac\uac01\ud615\uc758 \ub113\uc774\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"8911","problem_lang":"1","title":"Turtle","description":"<p><img alt=\"\" src=\"\/upload\/images\/turtle2(1).png\" style=\"float:right; height:139px; width:183px\" \/>You have a turtle robot moving in the two-dimensional Cartesian plane. The movement of this robot is determined by a sequence of the following commands:<\/p>\r\n\r\n<ol>\r\n\t<li>F: move forward just one unit<\/li>\r\n\t<li>B: move backward just one unit<\/li>\r\n\t<li>L: turn left 90 degree<\/li>\r\n\t<li>R: turn right 90 degree<\/li>\r\n<\/ol>\r\n\r\n<p>The last two commands, L and R, only change the orientation of the robot without changing its location. We will call the sequence of commands the control program of the turtle robot.&nbsp;<\/p>\r\n\r\n<p>You are to determine and estimate a portion of the plane that is large enough for the turtle s movement for a given control program. To make the problem simple, the portion is assumed to be a box whose edges are parallel to either the x- or y- axis of the Cartesian plane. More specifically, your program should calculate the size of the minimal bounding box which is large enough to encompass the trace of the movements of the turtle for a given control program.<\/p>\r\n\r\n<p>Let s think of an example. You may assume that the turtle is initially at the origin (0, 0) facing to the north, without loss of generality. If the control program is given as FLFRFLBRBLB, the turtle will move on the following track of the Cartesian plane:<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/turtle.png\" style=\"height:294px; width:304px\" \/><\/p>\r\n\r\n<p>Note that the dotted portion of the track denotes backward movement. As shown in the picture, the 2 2 gray box is enough to encompass the movement of the turtle. Therefore, your program should write 4, since the width and the height of the bounding box are both 2.<\/p>\r\n\r\n<p>Note that the trace of the turtle may not form a box in some cases. For instance, if the control program is given by FFLLFF, the turtle moves only on the y-axis. Therefore, the bounding box is not practically a box but a line segment, which implies that the width of the bounding box is zero. You program should output zero in such cases.<\/p>\r\n","input":"<p>Your program is to read the input 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 consists of a character string where each character denotes the control command. The string is given in a single line and consists only of four commands of the turtle robot. The length of the string is greater than 0 and no more than 500.<\/p>\r\n","output":"<p>Your program is to write to standard output. Print the area of the bounding box as a decimal integer in a single line for each test case.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ACM-ICPC > Regionals > Asia > Korea > Asia Regional - Daejeon 2011 L번