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문제

백범로에 있는 서강 은행의 본사는 2002년에 지어졌다. 2013년, 의장인 최준민은 은행 아트리움의 천장을 황금잎으로 재단장하기로 결심했다. (얼마 후 그는 소리소문없이 잠적해버렸다.)

새 천장은 평범하지 않아서, 아트리움의 일부가 기울어져 있었다. (그래서 아트리움은 더 커보였다) 아트리움의 크기와 기울어진 천장의 위치, 경사도는 정해지지 않았다.

준민이는 상범마법황금잎회사에서 천장과 기울어진 면을 장식할 황금잎을 얼마나 주문해야하는지 알고 싶었다. 또한 그는 비스듬한 부분이 천장이나 바닥과 닿는 것도 허가했다.

다음은 아트리움의 예제이다.

Note: 점선으로 그린 부분은 원래 박스를 나타내며, 빗금친 부분은 기울어진 부분을 표시한다.

빗금이 두번 쳐진 부분은 원래 천장 부분을 나타낸다. 벽과 바닥은 투명하다.

황금잎으로 덮을 부분은 천장과 기울어진 부분이다.

천장을 덮기 위해 얼마나 황금잎이 필요한지 계산하는 프로그램을 작성하시오.

입력

첫째줄은 데이터 세트의 개수를 나타내는 P(1 ≤ P ≤ 1000)가 입력으로 들어온다. 각각의 데이터 세트는 한 줄로 구성되어 있으며 L, W, H, A, B, C, D가 공백으로 구분되어 들어온다. L,W,H는 가로, 세로, 높이를 뜻하며 단위는 준민이다. (모두 양수) A,B,C,D는 다음 평면의 방정식의 계수로, 평면은 기울어진 부분을 나타낸다.

Ax + By + Cz = D

0 ≤ x ≤ L, 0 ≤ y ≤ W, 0 ≤ z ≤ H

원래 박스의 한쪽 끝은 항상 (0,0,0)에 위치하며 다른 쪽은 (L,W,H)에 위치한다. 평면은 수직이 되지 않으며 (C ≥ 1.0) 항상 박스 안쪽을 지나간다.

출력

각각의 데이터 세트에 대해 한 줄씩 천장을 덮기 위해 필요한 황금잎을 제곱준민 단위(정수)를 공백으로 구분하여 출력한다. (제곱준민 단위를 올림)

예제 입력 1

3
10 12 15 -1.3 1 1.1 3.5
10 12 10 -1.3 1 1.1 11
13 9 10 -1.3 1 1.1 0

예제 출력 1

166
164
144
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(\uadf8\ub798\uc11c \uc544\ud2b8\ub9ac\uc6c0\uc740 \ub354 \ucee4\ubcf4\uc600\ub2e4) \uc544\ud2b8\ub9ac\uc6c0\uc758 \ud06c\uae30\uc640 \uae30\uc6b8\uc5b4\uc9c4 \ucc9c\uc7a5\uc758 \uc704\uce58, \uacbd\uc0ac\ub3c4\ub294 \uc815\ud574\uc9c0\uc9c0 \uc54a\uc558\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\uc900\ubbfc\uc774\ub294 \uc0c1\ubc94\ub9c8\ubc95\ud669\uae08\uc78e\ud68c\uc0ac\uc5d0\uc11c \ucc9c\uc7a5\uacfc \uae30\uc6b8\uc5b4\uc9c4 \uba74\uc744 \uc7a5\uc2dd\ud560 \ud669\uae08\uc78e\uc744 \uc5bc\ub9c8\ub098 \uc8fc\ubb38\ud574\uc57c\ud558\ub294\uc9c0 \uc54c\uace0 \uc2f6\uc5c8\ub2e4. \ub610\ud55c \uadf8\ub294 \ube44\uc2a4\ub4ec\ud55c \ubd80\ubd84\uc774 \ucc9c\uc7a5\uc774\ub098 \ubc14\ub2e5\uacfc \ub2ff\ub294 \uac83\ub3c4 \ud5c8\uac00\ud588\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\ub2e4\uc74c\uc740 \uc544\ud2b8\ub9ac\uc6c0\uc758 \uc608\uc81c\uc774\ub2e4.<\/p>\r\n\r\n<p>\r\n\t<img alt=\"\" src=\"\/upload\/images\/ceil.png\" style=\"width: 603px; height: 202px;\" \/><\/p>\r\n\r\n<p>\r\n\tNote: \uc810\uc120\uc73c\ub85c \uadf8\ub9b0 \ubd80\ubd84\uc740 \uc6d0\ub798 \ubc15\uc2a4\ub97c \ub098\ud0c0\ub0b4\uba70, \ube57\uae08\uce5c \ubd80\ubd84\uc740 \uae30\uc6b8\uc5b4\uc9c4 \ubd80\ubd84\uc744 \ud45c\uc2dc\ud55c\ub2e4.<\/p>\r\n<p>\r\n\t\ube57\uae08\uc774 \ub450\ubc88 \uccd0\uc9c4 \ubd80\ubd84\uc740 \uc6d0\ub798 \ucc9c\uc7a5 \ubd80\ubd84\uc744 \ub098\ud0c0\ub0b8\ub2e4. \ubcbd\uacfc \ubc14\ub2e5\uc740 \ud22c\uba85\ud558\ub2e4.<\/p>\r\n<p>\r\n\t\ud669\uae08\uc78e\uc73c\ub85c \ub36e\uc744 \ubd80\ubd84\uc740 \ucc9c\uc7a5\uacfc \uae30\uc6b8\uc5b4\uc9c4 \ubd80\ubd84\uc774\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\ucc9c\uc7a5\uc744 \ub36e\uae30 \uc704\ud574 \uc5bc\ub9c8\ub098 \ud669\uae08\uc78e\uc774 \ud544\uc694\ud55c\uc9c0 \uacc4\uc0b0\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"\r\n<p>\r\n\t\uccab\uc9f8\uc904\uc740 \ub370\uc774\ud130 \uc138\ud2b8\uc758 \uac1c\uc218\ub97c \ub098\ud0c0\ub0b4\ub294 P(1 &le; P &le; 1000)\uac00 \uc785\ub825\uc73c\ub85c \ub4e4\uc5b4\uc628\ub2e4. \uac01\uac01\uc758 \ub370\uc774\ud130 \uc138\ud2b8\ub294 \ud55c \uc904\ub85c \uad6c\uc131\ub418\uc5b4 \uc788\uc73c\uba70 L, W, H, A, B, C, D\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \ub4e4\uc5b4\uc628\ub2e4. L,W,H\ub294 \uac00\ub85c, \uc138\ub85c, \ub192\uc774\ub97c \ub73b\ud558\uba70 \ub2e8\uc704\ub294 \uc900\ubbfc\uc774\ub2e4. (\ubaa8\ub450 \uc591\uc218) A,B,C,D\ub294 \ub2e4\uc74c \ud3c9\uba74\uc758 \ubc29\uc815\uc2dd\uc758 \uacc4\uc218\ub85c, \ud3c9\uba74\uc740 \uae30\uc6b8\uc5b4\uc9c4 \ubd80\ubd84\uc744 \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n\r\n<p>\r\n\tAx + By + Cz = D<\/p>\r\n<p>\r\n\t0 &le; x &le; L, 0 &le; y &le; W, 0 &le; z &le; H<\/p>\r\n\r\n<p>\r\n\t<p>\r\n\t\t\uc6d0\ub798 \ubc15\uc2a4\uc758 \ud55c\ucabd \ub05d\uc740 \ud56d\uc0c1 (0,0,0)\uc5d0 \uc704\uce58\ud558\uba70 \ub2e4\ub978 \ucabd\uc740 (L,W,H)\uc5d0 \uc704\uce58\ud55c\ub2e4. \ud3c9\uba74\uc740 \uc218\uc9c1\uc774 \ub418\uc9c0 \uc54a\uc73c\uba70 (C &ge;&nbsp;1.0) \ud56d\uc0c1 \ubc15\uc2a4 \uc548\ucabd\uc744 \uc9c0\ub098\uac04\ub2e4.<\/p>\r\n<\/p>\r\n\r\n\r\n","output":"<p>\r\n\t\uac01\uac01\uc758 \ub370\uc774\ud130 \uc138\ud2b8\uc5d0 \ub300\ud574 \ud55c \uc904\uc529 \ucc9c\uc7a5\uc744 \ub36e\uae30 \uc704\ud574 \ud544\uc694\ud55c \ud669\uae08\uc78e\uc744 \uc81c\uacf1\uc900\ubbfc \ub2e8\uc704(\uc815\uc218)\ub97c \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ud558\uc5ec \ucd9c\ub825\ud55c\ub2e4. (\uc81c\uacf1\uc900\ubbfc \ub2e8\uc704\ub97c \uc62c\ub9bc)<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2683","problem_lang":"1","title":"The Golden Ceiling","description":"<p>The main office of the Bank of Zork was built in the Aragain Village (later known as Flatheadia) in the year 722 of the Great Underground Empire (GUE). In 788 GUE, the chairman, J. Pierpont Flathead, decided (shortly before his unexplained disappearance in 789), that it was time to completely redesign the already ornate bank atrium with a ceiling covered in brilliant gold leaf.<\/p>\r\n\r\n<p>This new ceiling was not your ordinary ceiling. Although the atrium is essentially a big box, the ceiling would be slanted (supposedly, making the atrium look bigger). At the time, the exact dimensions of the rectangular atrium and the slope and location of the slanted ceiling had not been finalized. Flathead wanted to know how much gold leaf he would have to order from the Frobozz Magic Gold Leaf Company to cover the ceiling for different atrium dimensions and ceiling slants. He also wanted to allow the slanted part to possibly hit the floor of the box and\/or the top of the box.<\/p>\r\n\r\n<p>Consider the following rough sketches of some possible atrium configurations:<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/ceil.png\" style=\"height:202px; width:603px\" \/><\/p>\r\n\r\n<p>Note: The dashed outline represents the original box, the horizontally ruled surface is the slanted part of the ceiling and the cross hatched surface is the part of the top of the box not cut off by the plane. The walls and floor of the atrium are transparent. The total area to be covered (the ceiling) is the slanted part plus any part of the top of the original box that is not cut off by the plane.<\/p>\r\n\r\n<p>Your job is to write a program that Flathead could have used to calculate the amount gold leaf required to cover the ceiling for a particular configuration.<\/p>\r\n\r\n<p>As a sad epilogue, the main branch was brought to ruins when the Curse of Megaboz befell it in 883GUE. Between the barbarian invasions of the 880&#39;s and the countless looters that had tread the underground ruins in the years that followed, the entire bank with all its valuables, as well as its very expensive gold leaf ceiling, had been removed or vandalized. More information can be found on-line at: http:\/\/www.thezorklibrary.corn\/history\/bank_of_zork.html.<\/p>\r\n","input":"<p>The first line of input contains a single integer P, (1 &le; P &le; 1000), which is the number of data sets that follow. Each data set is a single line that contains the data set number, N, followed by a space, followed by seven space separated double precision floating point values, L, W, H, A, B, C and D. The values L, W and H specify the length, width and height of the atrium in Flathead Units (FU&#39;s), respectively, and are always positive values. The values A, B, C and D specify the coefficients of the plane equation for the slanted part of the ceiling:<\/p>\r\n\r\n<pre>\r\nAx + By + Cz = D<\/pre>\r\n\r\n<p>where: 0 &le; x &le; L, 0 &le; y &le; W, 0 &le; z &le; H.<\/p>\r\n\r\n<p>One corner of the original box is always at the origin (0, 0, 0) and the other at (L, W, H). The plane will never be vertical (C will be &ge; 1.0) and the plane will always pass through the interior of the box (there will be points (x, y, z) in the box and strictly above the plane ( Ax + BY + Cz &gt; D) and others strictly below the plane ( Ax + By + Cz &lt; D).<\/p>\r\n","output":"<p>For each data set there is one line of output. It contains the data set number (N) followed by a single space, followed by an integer value that is the number of square FU&#39;s required to cover the ceiling in gold leaf (rounded up to the next square FU).<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]