시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 70 5 5 29.412%

문제

아이폰 앱스토어에는 사용자들이 앱에 평점을 매길 수 있는 기능이 있다. 사용자는 별 한 개부터 다섯 개까지 평점을 매길 수 있다. 이러한 사용자의 평점이 모이면, 앱스토어는 그림과 같은 사용자 평점의 평균을 보여준다.

예를 들어, 사용자 세 명이 별 3개, 4개, 4개를 평가했으면, 평균 평점은 (3+4+4)/3 = 3.67 (소수점 셋째 자리에서 반올림) 이 된다.

위의 그림과 같이 총 126명이 평점을 매겼다면, 평균 평점은 \(\frac{53 \times 5+18 \times 4+ 11 \times 3 + 16 \times 2 + 28 \times 1}{126}=3.4126984\) (소수점 여덟째 자리에서 반올림) 이 된다.

상근이는 앱을 만들 때 마다 자신의 앱을 평가한 사람의 수와 각각의 별을 평가한 사람의 수, 평균 평점을 소수점 n(0 < n < 9)자리까지 데이터베이스에 저장해놨다. 어느날, 선영이는 상근이의 데이터베이스를 해킹했고, 평균 평점을 제외한 모든 정보를 삭제해버렸다.

남은 정보는 평균 평점 뿐이다. 이 정보를 이용해서 그러한 평균 평점을 만드려면 최소 몇 명이 앱을 평가해야 하는지를 구하는 프로그램을 작성하시오.

입력

입력은 여러 줄로 이루어져 있다. (최대 2000줄) 각 줄은 음이 아닌 소수점 v (1 ≤ v ≤ 5)가 주어진다. v는 소수점 최소 한 자리, 최대 여덟 자리이다. v은 n자리 바로 다음 자리에서 반올림한 값이다.

입력의 마지막 줄에는 음수가 주어진다.

출력

입력으로 주어지는 평균 평점마다 그러한 평균 평점을 만들기 위해 최소 몇 명이 필요한지 출력한다.

예제 입력 1

1.15
4.56316411
4.56316
3.67
3.66
-1.00

예제 출력 1

Case 1: 13
Case 2: 847
Case 3: 190
Case 4: 3
Case 5: 29
[{"problem_id":"5655","problem_lang":"0","title":"\ud3c9\uc810","description":"<p>\uc544\uc774\ud3f0 \uc571\uc2a4\ud1a0\uc5b4\uc5d0\ub294 \uc0ac\uc6a9\uc790\ub4e4\uc774 \uc571\uc5d0 \ud3c9\uc810\uc744 \ub9e4\uae38 \uc218 \uc788\ub294 \uae30\ub2a5\uc774 \uc788\ub2e4. \uc0ac\uc6a9\uc790\ub294 \ubcc4 \ud55c \uac1c\ubd80\ud130 \ub2e4\uc12f \uac1c\uae4c\uc9c0 \ud3c9\uc810\uc744 \ub9e4\uae38 \uc218 \uc788\ub2e4. \uc774\ub7ec\ud55c \uc0ac\uc6a9\uc790\uc758 \ud3c9\uc810\uc774 \ubaa8\uc774\uba74, \uc571\uc2a4\ud1a0\uc5b4\ub294 \uadf8\ub9bc\uacfc \uac19\uc740 \uc0ac\uc6a9\uc790 \ud3c9\uc810\uc758 \ud3c9\uade0\uc744 \ubcf4\uc5ec\uc900\ub2e4.<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, \uc0ac\uc6a9\uc790 \uc138 \uba85\uc774 \ubcc4 3\uac1c, 4\uac1c, 4\uac1c\ub97c \ud3c9\uac00\ud588\uc73c\uba74, \ud3c9\uade0 \ud3c9\uc810\uc740 (3+4+4)\/3 = 3.67 (\uc18c\uc218\uc810 \uc14b\uc9f8 \uc790\ub9ac\uc5d0\uc11c \ubc18\uc62c\ub9bc) \uc774 \ub41c\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/rating.png\" style=\"height:163px; width:575px\" \/><\/p>\r\n\r\n<p>\uc704\uc758 \uadf8\ub9bc\uacfc \uac19\uc774 \ucd1d 126\uba85\uc774 \ud3c9\uc810\uc744 \ub9e4\uacbc\ub2e4\uba74, \ud3c9\uade0 \ud3c9\uc810\uc740 \\(\\frac{53 \\times 5+18 \\times 4+ 11 \\times 3 + 16 \\times 2 + 28 \\times 1}{126}=3.4126984\\) (\uc18c\uc218\uc810 \uc5ec\ub35f\uc9f8 \uc790\ub9ac\uc5d0\uc11c \ubc18\uc62c\ub9bc) \uc774 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc0c1\uadfc\uc774\ub294 \uc571\uc744 \ub9cc\ub4e4 \ub54c \ub9c8\ub2e4 \uc790\uc2e0\uc758 \uc571\uc744 \ud3c9\uac00\ud55c \uc0ac\ub78c\uc758 \uc218\uc640 \uac01\uac01\uc758 \ubcc4\uc744 \ud3c9\uac00\ud55c \uc0ac\ub78c\uc758 \uc218, \ud3c9\uade0 \ud3c9\uc810\uc744 \uc18c\uc218\uc810 n(0 &lt; n &lt; 9)\uc790\ub9ac\uae4c\uc9c0 \ub370\uc774\ud130\ubca0\uc774\uc2a4\uc5d0 \uc800\uc7a5\ud574\ub1a8\ub2e4. \uc5b4\ub290\ub0a0, \uc120\uc601\uc774\ub294 \uc0c1\uadfc\uc774\uc758 \ub370\uc774\ud130\ubca0\uc774\uc2a4\ub97c \ud574\ud0b9\ud588\uace0, \ud3c9\uade0 \ud3c9\uc810\uc744 \uc81c\uc678\ud55c \ubaa8\ub4e0 \uc815\ubcf4\ub97c \uc0ad\uc81c\ud574\ubc84\ub838\ub2e4.<\/p>\r\n\r\n<p>\ub0a8\uc740 \uc815\ubcf4\ub294 \ud3c9\uade0 \ud3c9\uc810 \ubfd0\uc774\ub2e4. \uc774 \uc815\ubcf4\ub97c \uc774\uc6a9\ud574\uc11c \uadf8\ub7ec\ud55c \ud3c9\uade0 \ud3c9\uc810\uc744 \ub9cc\ub4dc\ub824\uba74 \ucd5c\uc18c \uba87 \uba85\uc774 \uc571\uc744 \ud3c9\uac00\ud574\uc57c \ud558\ub294\uc9c0\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \uc5ec\ub7ec \uc904\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. (\ucd5c\ub300 2000\uc904) \uac01 \uc904\uc740 \uc74c\uc774 \uc544\ub2cc \uc18c\uc218\uc810 v (1 &le; v &le; 5)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. v\ub294 \uc18c\uc218\uc810 \ucd5c\uc18c \ud55c \uc790\ub9ac, \ucd5c\ub300 \uc5ec\ub35f \uc790\ub9ac\uc774\ub2e4. v\uc740 n\uc790\ub9ac \ubc14\ub85c \ub2e4\uc74c \uc790\ub9ac\uc5d0\uc11c \ubc18\uc62c\ub9bc\ud55c \uac12\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc785\ub825\uc758 \ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 \uc74c\uc218\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c0\ub294 \ud3c9\uade0 \ud3c9\uc810\ub9c8\ub2e4 \uadf8\ub7ec\ud55c \ud3c9\uade0 \ud3c9\uc810\uc744 \ub9cc\ub4e4\uae30 \uc704\ud574 \ucd5c\uc18c \uba87 \uba85\uc774 \ud544\uc694\ud55c\uc9c0 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"5655","problem_lang":"1","title":"Rating Hazard","description":"<p>A very important aspect of web portals is customer reviews. The customers can rate any product in the web portal. Generally, a customer can rate a product from one star to five star. Based on the rating of all the customers the average customer rating for a product is shown. Look at the figure on the left to get a clear idea. For example if three customers rate a product as 3 star, 4 star and 4 star respectively then the average rating will be (3+4+4)\/3 = 3.67 (Rounded to two digits after the decimal point). In the figure on the below 126 customers have rated a product and 53, 18, 11, 16 and 28&nbsp;customers have rated the product as 5 star, 4 star, 3 star, 2 star and 1 star respectively. So the average rating is: \\(\\frac{53 \\times 5+18 \\times 4+ 11 \\times 3 + 16 \\times 2 + 28 \\times 1}{126}=3.41269841\\) (Rounded to eight digits after the decimal point).<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/rating.png\" style=\"height:163px; width:575px\" \/><\/p>\r\n\r\n<p>Most web portals display the total number of people who have rated the product (As more people rates the product the more reliable the rating is) but do not display the numeric value of the average rating. In the web portal of warzone (A renowned web portal) the total number of customers that have rated a product (In the figure above the total 126 customers have rated the product) and the average rating is stored in two different tables. The average rating is stored, rounded to n (0&lt;n&lt;9) digits after the decimal point so its value is not always the exact average value. Unfortunately, the table that stored the total number of people that rated different products somehow got corrupted. All information available in the database now is the average rating (rounded to at most eight digits after the decimal point). They do not want to lose the huge number of customer ratings they have received throughout 10-15 years but also they cannot cheat with their customers by guessing the number of raters or voters. So from the average rating they want to determine the minimum possible number of people that rated that product. You have to help them find it out by writing a program.<\/p>\r\n","input":"<p>The input can contain up to 2000 lines of inputs. Each line contains a non-negative floating point number v (1 &le; v &le; 5). This number will have minimum one digit and maximum eight digits after the decimal point. If this number has n digits after the decimal point then you have to assume that the value of the average is given rounded to n digits after the decimal point.<\/p>\r\n\r\n<p>Input is terminated by a line containing a negative number.<\/p>\r\n","output":"<p>For each line of input produce one line of output. This line contains the serial of output followed by an integer T which denotes the minimum number of voter that is required for this average rating.&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]