시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 299 257 246 86.620%

문제

숫자 맞추기 게임은 초등학교 학생들 사이에서 유행하는 게임이다. 선생님은 학생들의 연산 실력과 논리적인 사고력을 기르기위해 학생들에게 이 게임을 권유하고 있다.

이 게임을 시작할 때는 친구가 숫자 하나를 머리속에 생각해야 한다. 이 숫자를 n0이라고 하자. 그러고 나서 다음과 같이 게임을 진행한다.

  1. 친구에게 n1 = 3*n0 계산을 하라고 한 뒤, n1이 짝수인지 홀수인지를 말해달라고 한다.
  2. n1이 짝수라면, n2 = n1/2를, 홀수라면 n2 = (n1+1)/2를 계산해달라고 한다.
  3. n3 = 3*n2의 계산을 부탁한다.
  4. 친구에게 n4 = n3/9를 계산한 뒤, 그 값을 말해달라고 한다. (n4는 나눗셈의 몫이다)
  5. 자 이제, n1이 짝수였다면, n0 = 2*n4로, 홀수였다면, n0 = 2*n4+1로 처음 친구가 생각한 숫자를 맞출 수 있다.

예를 들어,  친구가 생각한 수가 n0=37이었다면, n1 = 111이 되고 홀수이다. 그 다음 n2 = 56, n3 = 168, n4 = 18이 된다. 친구는 n4를 알려주게 된다. 

그럼 2*n4+1 = 37이기 때문에, 친구가 제일 처음 생각한 숫자를 맞출 수 있다.

n0이 주어졌을 때, n1이 홀수인지 짝수인지와 n4를 구하는 프로그램을 작성하시오.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다. 각 테스트 케이스는 한 줄로 이루어져 있고, n0으로 이루어져 있다. (0 < n0 < 1,000,000) 입력의 마지막 줄에는 0이 하나 주어진다.

출력

각 테스트 케이스에 대해서, 케이스 번호를 출력하고 n1이 짝수라면 'even', 홀수라면 'odd'를 출력하고, n4를 출력한다.

예제 입력 1

37
38
0

예제 출력 1

1. odd 18
2. even 19
[{"problem_id":"4892","problem_lang":"0","title":"\uc22b\uc790 \ub9de\ucd94\uae30 \uac8c\uc784","description":"<p>\uc22b\uc790 \ub9de\ucd94\uae30 \uac8c\uc784\uc740 \ucd08\ub4f1\ud559\uad50 \ud559\uc0dd\ub4e4 \uc0ac\uc774\uc5d0\uc11c \uc720\ud589\ud558\ub294 \uac8c\uc784\uc774\ub2e4. \uc120\uc0dd\ub2d8\uc740 \ud559\uc0dd\ub4e4\uc758 \uc5f0\uc0b0 \uc2e4\ub825\uacfc \ub17c\ub9ac\uc801\uc778 \uc0ac\uace0\ub825\uc744 \uae30\ub974\uae30\uc704\ud574 \ud559\uc0dd\ub4e4\uc5d0\uac8c \uc774 \uac8c\uc784\uc744 \uad8c\uc720\ud558\uace0 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc774 \uac8c\uc784\uc744 \uc2dc\uc791\ud560 \ub54c\ub294 \uce5c\uad6c\uac00 \uc22b\uc790 \ud558\ub098\ub97c \uba38\ub9ac\uc18d\uc5d0 \uc0dd\uac01\ud574\uc57c \ud55c\ub2e4. \uc774 \uc22b\uc790\ub97c n<sub>0<\/sub>\uc774\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uace0 \ub098\uc11c \ub2e4\uc74c\uacfc \uac19\uc774 \uac8c\uc784\uc744 \uc9c4\ud589\ud55c\ub2e4.<\/p>\r\n\r\n<ol>\r\n\t<li>\uce5c\uad6c\uc5d0\uac8c n<sub>1<\/sub> = 3*n<sub>0<\/sub> \uacc4\uc0b0\uc744 \ud558\ub77c\uace0 \ud55c \ub4a4, n<sub>1<\/sub>\uc774 \uc9dd\uc218\uc778\uc9c0 \ud640\uc218\uc778\uc9c0\ub97c \ub9d0\ud574\ub2ec\ub77c\uace0 \ud55c\ub2e4.<\/li>\r\n\t<li>n<sub>1<\/sub>\uc774 \uc9dd\uc218\ub77c\uba74, n<sub>2<\/sub> = n<sub>1<\/sub>\/2\ub97c, \ud640\uc218\ub77c\uba74 n<sub>2<\/sub> = (n<sub>1<\/sub>+1)\/2\ub97c \uacc4\uc0b0\ud574\ub2ec\ub77c\uace0 \ud55c\ub2e4.<\/li>\r\n\t<li>n<sub>3<\/sub> = 3*n<sub>2<\/sub>\uc758 \uacc4\uc0b0\uc744 \ubd80\ud0c1\ud55c\ub2e4.<\/li>\r\n\t<li>\uce5c\uad6c\uc5d0\uac8c n<sub>4<\/sub> = n<sub>3<\/sub>\/9\ub97c \uacc4\uc0b0\ud55c \ub4a4, \uadf8 \uac12\uc744 \ub9d0\ud574\ub2ec\ub77c\uace0 \ud55c\ub2e4. (n<sub>4<\/sub>\ub294 \ub098\ub217\uc148\uc758 \ubaab\uc774\ub2e4)<\/li>\r\n\t<li>\uc790 \uc774\uc81c, n<sub>1<\/sub>\uc774 \uc9dd\uc218\uc600\ub2e4\uba74, n<sub>0<\/sub> = 2*n<sub>4<\/sub>\ub85c, \ud640\uc218\uc600\ub2e4\uba74, n<sub>0<\/sub> = 2*n<sub>4<\/sub>+1\ub85c \ucc98\uc74c \uce5c\uad6c\uac00 \uc0dd\uac01\ud55c \uc22b\uc790\ub97c \ub9de\ucd9c \uc218 \uc788\ub2e4.<\/li>\r\n<\/ol>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, &nbsp;\uce5c\uad6c\uac00 \uc0dd\uac01\ud55c \uc218\uac00 n<sub>0<\/sub>=37\uc774\uc5c8\ub2e4\uba74, n<sub>1<\/sub> = 111\uc774 \ub418\uace0 \ud640\uc218\uc774\ub2e4. \uadf8 \ub2e4\uc74c n<sub>2<\/sub> = 56, n<sub>3<\/sub> = 168, n<sub>4<\/sub> = 18\uc774 \ub41c\ub2e4. \uce5c\uad6c\ub294 n<sub>4<\/sub>\ub97c \uc54c\ub824\uc8fc\uac8c \ub41c\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\uadf8\ub7fc 2*n<sub>4<\/sub>+1 = 37\uc774\uae30 \ub54c\ubb38\uc5d0, \uce5c\uad6c\uac00 \uc81c\uc77c \ucc98\uc74c \uc0dd\uac01\ud55c \uc22b\uc790\ub97c \ub9de\ucd9c \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>n<sub>0<\/sub>\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, n<sub>1<\/sub>\uc774 \ud640\uc218\uc778\uc9c0 \uc9dd\uc218\uc778\uc9c0\uc640 n<sub>4<\/sub>\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \uc5ec\ub7ec \uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \ud55c \uc904\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uace0, n<sub>0<\/sub>\uc73c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. (0 &lt; n<sub>0<\/sub> &lt; 1,000,000) \uc785\ub825\uc758 \ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 0\uc774 \ud558\ub098 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574\uc11c, \ucf00\uc774\uc2a4 \ubc88\ud638\ub97c \ucd9c\ub825\ud558\uace0 n<sub>1<\/sub>\uc774 \uc9dd\uc218\ub77c\uba74 &#39;even&#39;, \ud640\uc218\ub77c\uba74 &#39;odd&#39;\ub97c \ucd9c\ub825\ud558\uace0, n<sub>4<\/sub>\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"4892","problem_lang":"1","title":"Probability One","description":"<p>Number guessing is a popular game between elementary-school kids. Teachers encourage pupils to play the game as it enhances their arithmetic skills, logical thinking, and following-up simple procedures. We think that, most probably, you too will master in few minutes. Here&rsquo;s one example of how you too can play this game: Ask a friend to think of a number, let&rsquo;s call it n<sub>0<\/sub>. Then:<\/p>\r\n\r\n<ol>\r\n\t<li>Ask your friend to compute n<sub>1<\/sub> = 3 * n<sub>0<\/sub> and to tell you if n<sub>1<\/sub> is even or odd<\/li>\r\n\t<li>If n<sub>1<\/sub> is even, ask your friend to compute n<sub>2<\/sub> = n<sub>1<\/sub>\/2. If, otherwise, n<sub>1<\/sub> was odd then let your friend compute n<sub>2<\/sub> = (n<sub>1<\/sub> + 1)\/2.<\/li>\r\n\t<li>Now ask your friend to calculate n<sub>3<\/sub> = 3 * n<sub>2<\/sub>.<\/li>\r\n\t<li>Ask your friend to tell tell you the result of n<sub>4<\/sub> = n<sub>3<\/sub>\/9. (n<sub>4<\/sub> is the quotient of the division operation. In computer lingo, &rsquo;\/&rsquo; is the integer-division operator.)<\/li>\r\n\t<li>Now you can simply reveal the original number by calculating n<sub>0<\/sub> = 2 * n<sub>4<\/sub> if n<sub>1<\/sub> was even, or n<sub>0<\/sub> = 2 * n<sub>4<\/sub> + 1 otherwise.<\/li>\r\n<\/ol>\r\n\r\n<p>Here&rsquo;s an example that you can follow: If n<sub>0<\/sub> = 37, then n<sub>1<\/sub> = 111 which is odd. Now we can calculate n<sub>2<\/sub> = 56, n<sub>3<\/sub> = 168, and n<sub>4<\/sub> = 18, which is what your friend will tell you. Doing the calculation 2 &times; n<sub>4<\/sub> + 1 = 37 reveals n<sub>0<\/sub>.<\/p>\r\n","input":"<p>Your program will be tested on one or more test cases. Each test case is made of a single positive number (0 &lt; n<sub>0<\/sub> &lt; 1, 000, 000).<\/p>\r\n\r\n<p>The last line of the input \ufb01le has a single zero (which is not part of the test cases.)<\/p>\r\n","output":"<p>For each test case, print the following line:<\/p>\r\n\r\n<pre>\r\nk. B Q<\/pre>\r\n\r\n<p>Where k is the test case number (starting at one,) B is either &rsquo;even&rsquo; or &rsquo;odd&rsquo; (without the quotes) depending on your friend&rsquo;s answer in step 1. Q is your friend&rsquo;s answer to step 4.<\/p>\r\n","hint":"<p>For each test case, print the following line:<\/p>\r\n\r\n<pre>\r\nk. B Q<\/pre>\r\n\r\n<p>Where k is the test case number (starting at one,) B is either &rsquo;even&rsquo; or &rsquo;odd&rsquo; (without the quotes) depending on your friend&rsquo;s answer in step 1. Q is your friend&rsquo;s answer to step 4.<\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]