시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 27 9 5 29.412%

문제

유리수는 두 정수의 비로 나타낼 수 있다. 분자(n)와 분모(d)가 주어지면 이 분수를 n/d으로 쓴다. 유리수의 표현 방법은 유일하지 않다. 예를 들어, 1/2과 2/4는 그 값이 같다. 어떤 유리수 표현법 n/d이 gcd(|n|, |d|) = 1이라면 이것이 "기약분수로 표현되었다"라고 한다. 따라서 1/2은 기약분수로 표현되었지만 2/4는 아니다.

유리수의 덧셈은 다음과 같이 정의된다. 오른쪽 항이 기약분수로 표현될 필요는 없다는 점에 주목하라.

\[\frac{n_1}{d_1} + \frac{n_2}{d_2} = \frac{n_1d_2 + n_2d_1}{d_1d_2}\]

분자가 분모보다 크거나 같은 유리수는 대분수 꼴로 표현할 수 있는데, 이것은 정수부와 소수부로 이루어 진다. 예를 들어, $5 {{1}\over{3}}$은 16/3과 같은 값을 가지는 대분수 표현이다.

당신이 할 일은 유리수열을 읽어 그 합을 출력하는 것이다.

입력

입력은 몇 개의 테스트로 구성된다. 각 테스트의 정보는 첫 줄에 n(1 ≤ n < 1000)을 포함한다. n = 0인 경우 입력이 끝난다.

다음 n개의 줄은 공백이 없는 하나의 문자열이다. 각 문자열은 유리수 하나를 나타내며, 다음 세 형태 중 하나이고 기약분수로 표현되지 않을 수 있다 (w, n과 d는 정수이다: 0 ≤ w,n < 1000, 1 ≤ d < 1000).

  • w,n/d: (w * d + n) / d와 값이 같은 대분수
  • n/d: 정수부가 0인 유리수
  • w: 소수부가 0인 정수

출력

출력은 화면에 나온 대로 테스트 번호를 포함하여 합을 출력한다. 만약 합의 정수부나 소수부가 없다면 각 부분을 생략하여 출력한다. 특수한 경우로, 정수부와 소수부가 모두 없다면 0을 출력해야 한다.

예제 입력 1

2
1/2
1/3
3
1/3
2/6
3/9
3
1
2/3
4,5/6
0

예제 출력 1

Test 1: 5/6
Test 2: 1
Test 3: 6,1/2

힌트

[{"problem_id":"9215","problem_lang":"0","title":"\uc2e0\ub098\ub294 \ubd84\uc218 \uacc4\uc0b0","description":"<p>\uc720\ub9ac\uc218\ub294 \ub450 \uc815\uc218\uc758 \ube44\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4. \ubd84\uc790(n)\uc640&nbsp;\ubd84\ubaa8(d)\uac00 \uc8fc\uc5b4\uc9c0\uba74 \uc774 \ubd84\uc218\ub97c n\/d\uc73c\ub85c \uc4f4\ub2e4. \uc720\ub9ac\uc218\uc758 \ud45c\ud604 \ubc29\ubc95\uc740 \uc720\uc77c\ud558\uc9c0 \uc54a\ub2e4. \uc608\ub97c \ub4e4\uc5b4, 1\/2\uacfc&nbsp;2\/4\ub294 \uadf8 \uac12\uc774 \uac19\ub2e4. \uc5b4\ub5a4 \uc720\ub9ac\uc218 \ud45c\ud604\ubc95 n\/d\uc774 gcd(|n|, |d|) = 1\uc774\ub77c\uba74 \uc774\uac83\uc774 &quot;\uae30\uc57d\ubd84\uc218\ub85c \ud45c\ud604\ub418\uc5c8\ub2e4&quot;\ub77c\uace0 \ud55c\ub2e4. \ub530\ub77c\uc11c 1\/2\uc740&nbsp;\uae30\uc57d\ubd84\uc218\ub85c \ud45c\ud604\ub418\uc5c8\uc9c0\ub9cc 2\/4\ub294 \uc544\ub2c8\ub2e4.<\/p>\r\n\r\n<p>\uc720\ub9ac\uc218\uc758 \ub367\uc148\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ub41c\ub2e4. \uc624\ub978\ucabd \ud56d\uc774 \uae30\uc57d\ubd84\uc218\ub85c \ud45c\ud604\ub420 \ud544\uc694\ub294 \uc5c6\ub2e4\ub294 \uc810\uc5d0 \uc8fc\ubaa9\ud558\ub77c.<\/p>\r\n\r\n<p>\\[\\frac{n_1}{d_1} + \\frac{n_2}{d_2} = \\frac{n_1d_2 + n_2d_1}{d_1d_2}\\]<\/p>\r\n\r\n<p>\ubd84\uc790\uac00 \ubd84\ubaa8\ubcf4\ub2e4 \ud06c\uac70\ub098 \uac19\uc740 \uc720\ub9ac\uc218\ub294 \ub300\ubd84\uc218 \uaf34\ub85c \ud45c\ud604\ud560 \uc218 \uc788\ub294\ub370, \uc774\uac83\uc740 \uc815\uc218\ubd80\uc640 \uc18c\uc218\ubd80\ub85c \uc774\ub8e8\uc5b4 \uc9c4\ub2e4. \uc608\ub97c \ub4e4\uc5b4, $5 {{1}\\over{3}}$\uc740&nbsp;16\/3\uacfc \uac19\uc740 \uac12\uc744 \uac00\uc9c0\ub294 \ub300\ubd84\uc218 \ud45c\ud604\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub2f9\uc2e0\uc774 \ud560 \uc77c\uc740 \uc720\ub9ac\uc218\uc5f4\uc744 \uc77d\uc5b4 \uadf8 \ud569\uc744 \ucd9c\ub825\ud558\ub294 \uac83\uc774\ub2e4.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \uba87 \uac1c\uc758 \ud14c\uc2a4\ud2b8\ub85c \uad6c\uc131\ub41c\ub2e4. \uac01 \ud14c\uc2a4\ud2b8\uc758 \uc815\ubcf4\ub294 \uccab \uc904\uc5d0&nbsp;n(1 &le; n&nbsp;&lt; 1000)\uc744 \ud3ec\ud568\ud55c\ub2e4. n = 0\uc778 \uacbd\uc6b0 \uc785\ub825\uc774 \ub05d\ub09c\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c n\uac1c\uc758 \uc904\uc740 \uacf5\ubc31\uc774 \uc5c6\ub294 \ud558\ub098\uc758 \ubb38\uc790\uc5f4\uc774\ub2e4. \uac01 \ubb38\uc790\uc5f4\uc740 \uc720\ub9ac\uc218 \ud558\ub098\ub97c \ub098\ud0c0\ub0b4\uba70, \ub2e4\uc74c \uc138 \ud615\ud0dc \uc911 \ud558\ub098\uc774\uace0 \uae30\uc57d\ubd84\uc218\ub85c \ud45c\ud604\ub418\uc9c0 \uc54a\uc744 \uc218 \uc788\ub2e4 (w, n\uacfc d\ub294 \uc815\uc218\uc774\ub2e4: 0 &le; w,n &lt; 1000, 1 &le; d &lt; 1000).<\/p>\r\n\r\n<ul>\r\n\t<li>w,n\/d: (w * d +&nbsp;n) \/ d\uc640 \uac12\uc774 \uac19\uc740 \ub300\ubd84\uc218<\/li>\r\n\t<li>n\/d: \uc815\uc218\ubd80\uac00 0\uc778 \uc720\ub9ac\uc218<\/li>\r\n\t<li>w: \uc18c\uc218\ubd80\uac00 0\uc778 \uc815\uc218<\/li>\r\n<\/ul>\r\n","output":"<p>\ucd9c\ub825\uc740 \ud654\uba74\uc5d0 \ub098\uc628 \ub300\ub85c \ud14c\uc2a4\ud2b8 \ubc88\ud638\ub97c \ud3ec\ud568\ud558\uc5ec \ud569\uc744 \ucd9c\ub825\ud55c\ub2e4. \ub9cc\uc57d \ud569\uc758 \uc815\uc218\ubd80\ub098 \uc18c\uc218\ubd80\uac00 \uc5c6\ub2e4\uba74 \uac01 \ubd80\ubd84\uc744 \uc0dd\ub7b5\ud558\uc5ec \ucd9c\ub825\ud55c\ub2e4. \ud2b9\uc218\ud55c \uacbd\uc6b0\ub85c, \uc815\uc218\ubd80\uc640 \uc18c\uc218\ubd80\uac00 \ubaa8\ub450 \uc5c6\ub2e4\uba74 0\uc744 \ucd9c\ub825\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"9215","problem_lang":"1","title":"Fun With Fractions","description":"<p>A rational number can be represented as the ratio of two integers, referred to as the numerator (n) and the denominator (d) and written n\/d. A rational number&#39;s representation is not unique. For example the rational numbers 1\/2 and 2\/4 are equivalent. A rational number representation is described as &quot;in lowest terms&quot; if the numerator and denominator have no common factors. Thus 1\/2 is in lowest terms but 2\/4 is not. A rational number can be reduced to lowest terms by dividing by the greatest common divisor of n and d.<\/p>\r\n\r\n<p>Addition of rational numbers is defined as follows. Note that the right hand side of this equality will not necessarily be in lowest terms.<\/p>\r\n\r\n<p>\\[\\frac{n_1}{d_1} + \\frac{n_2}{d_2} = \\frac{n_1d_2 + n_2d_1}{d_1d_2}\\]<\/p>\r\n\r\n<p>A rational number for which the numerator is greater than or equal to the denominator can be displayed in mixed format, which includes a whole number part and a fractional part. For example, $5 {{1}\\over{3}}$ is a mixed format representation of the rational number 16\/3.<\/p>\r\n\r\n<p>Your task is to write a program that reads a sequence of rational numbers and displays their sum.<\/p>\r\n","input":"<p>Input will consist of specifications for a series of tests. Information for each test begins with a line containing a single integer 1 &lt;= n &lt; 1000 indicating how many values follow. A count of zero terminates the input.<\/p>\r\n\r\n<p>The n following lines each contain a single string with no embedded whitespace . Each string represents a rational number, which could be in any of the following forms and will not necessarily be in lowest terms (w, n, and d are integers: 0 &lt;= w,n &lt; 1000, 1 &lt;= d &lt; 1000).<\/p>\r\n\r\n<ul>\r\n\t<li>w,n\/d: a mixed number equivalent to the rational number (w*d + n) \/ d.<\/li>\r\n\t<li>n\/d: a rational number with a zero whole number part<\/li>\r\n\t<li>w: a whole number with a zero fractional part<\/li>\r\n<\/ul>\r\n","output":"<p>Output should consist of one line for each test comprising the test number (formatted as shown) followed by a single space and the sum of the input number sequence. The sum should be displayed in lowest terms using mixed number format. If either the whole number part or the fractional part is zero, that part should be omitted. As a special case, if both parts are zero, the value should be displayed as a single 0.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]