시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 128 MB 10 8 6 100.000%

문제

7로 나누었을 때, 나머지가 1 또는 6인 숫자를 7N+{1,6} 숫자라고 한다. 하지만, 발음하기 어려우므로 이러한 숫자를 월요일-토요일 숫자라고 하자.

월요일-토요일 숫자 a와 b가 있을 때, ax = b를 만족하는 월요일-토요일 숫자 x가 있다면, a를 b의 월요일-토요일 약수라고 한다. 사실, 월요일-토요일 숫자 a가 b의 약수(일반적인 약수)라면, a는 b의 월요일-토요일 약수이다. 또, 역도 성립한다.

월요일-토요일 소수란 1보다 큰 월요일-토요일 숫자가 1과 자기 자신을 제외하고 월요일-토요일 약수가 없는 수이다. 월요일-토요일 숫자가 소수일 때, 이 수는 월요일-토요일 소수이다. 하지만, 그 역은 성립하지 않는다. 예를 들어, 27은 월요일-토요일 소수이지만, 소수는 아니다.

어떤 월요일-토요일 숫자의 월요일-토요일 약수 중에서 월요일-토요일 소수인 것을 월요일-토요일 소인수라고 한다. 예를 들어, 27은 216의 월요일-토요일 소인수이다. (216 = 27 * 8)

1보다 큰 월요일-토요일 솟자는 하나 또는 그 이상의 월요일-토요일 소수의 곱으로 나타낼 수 있다. 이러한 표현은 유일하지 않다. 예를 들어, 216 = 6 * 6 * 6 = 8 * 27이다.

월요일-토요일 숫자가 주어졌을 때, 월요일-토요일 소인수를 모두 구하는 프로그램을 작성하시오.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다. 각 테스트 케이스는 한 줄로 이루어져 있고, 월요일-토요일 수가 주어진다. 이 수는 1보다 크고, 300000보다 작다. 입력의 마지막 줄에는 1이 주어진다.

출력

입력으로 주어진 월요일-토요일 숫자에 대해서, 그 숫자를 출력하고, ":"을 출력한 다음에 월요일-토요일 소인수를 오름차순으로 출력한다. 모든 월요일-토요일 소인수 앞에는 공백을 한 칸 출력해야 한다.

예제 입력 1

205920
262144
262200
279936
299998
1

예제 출력 1

205920: 6 8 13 15 20 22 55 99
262144: 8
262200: 6 8 15 20 50 57 69 76 92 190 230 475 575 874 2185
279936: 6 8 27
299998: 299998

힌트

[{"problem_id":"4969","problem_lang":"0","title":"\uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c","description":"<p>\r\n\t7\ub85c \ub098\ub204\uc5c8\uc744 \ub54c, \ub098\uba38\uc9c0\uac00 1 \ub610\ub294 6\uc778 \uc22b\uc790\ub97c 7N+{1,6} \uc22b\uc790\ub77c\uace0 \ud55c\ub2e4. \ud558\uc9c0\ub9cc, \ubc1c\uc74c\ud558\uae30 \uc5b4\ub824\uc6b0\ubbc0\ub85c \uc774\ub7ec\ud55c \uc22b\uc790\ub97c \uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc22b\uc790\ub77c\uace0 \ud558\uc790.<\/p>\r\n\r\n<p>\r\n\t\uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc22b\uc790 a\uc640 b\uac00 \uc788\uc744 \ub54c, ax = b\ub97c \ub9cc\uc871\ud558\ub294 \uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc22b\uc790 x\uac00 \uc788\ub2e4\uba74, a\ub97c b\uc758 \uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc57d\uc218\ub77c\uace0 \ud55c\ub2e4. \uc0ac\uc2e4, \uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc22b\uc790 a\uac00 b\uc758 \uc57d\uc218(\uc77c\ubc18\uc801\uc778 \uc57d\uc218)\ub77c\uba74, a\ub294 b\uc758 \uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc57d\uc218\uc774\ub2e4. \ub610, \uc5ed\ub3c4 \uc131\ub9bd\ud55c\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc18c\uc218\ub780 1\ubcf4\ub2e4 \ud070 \uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc22b\uc790\uac00 1\uacfc \uc790\uae30 \uc790\uc2e0\uc744 \uc81c\uc678\ud558\uace0 \uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc57d\uc218\uac00 \uc5c6\ub294 \uc218\uc774\ub2e4. \uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc22b\uc790\uac00 \uc18c\uc218\uc77c \ub54c, \uc774 \uc218\ub294 \uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc18c\uc218\uc774\ub2e4. \ud558\uc9c0\ub9cc, \uadf8 \uc5ed\uc740 \uc131\ub9bd\ud558\uc9c0 \uc54a\ub294\ub2e4. \uc608\ub97c \ub4e4\uc5b4, 27\uc740 \uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc18c\uc218\uc774\uc9c0\ub9cc, \uc18c\uc218\ub294 \uc544\ub2c8\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\uc5b4\ub5a4 \uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc22b\uc790\uc758 \uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc57d\uc218 \uc911\uc5d0\uc11c \uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc18c\uc218\uc778 \uac83\uc744 \uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc18c\uc778\uc218\ub77c\uace0 \ud55c\ub2e4. \uc608\ub97c \ub4e4\uc5b4, 27\uc740 216\uc758 \uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc18c\uc778\uc218\uc774\ub2e4. (216 = 27 * 8)<\/p>\r\n\r\n<p>\r\n\t1\ubcf4\ub2e4 \ud070 \uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc19f\uc790\ub294 \ud558\ub098 \ub610\ub294 \uadf8 \uc774\uc0c1\uc758 \uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc18c\uc218\uc758 \uacf1\uc73c\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4. \uc774\ub7ec\ud55c \ud45c\ud604\uc740 \uc720\uc77c\ud558\uc9c0 \uc54a\ub2e4. \uc608\ub97c \ub4e4\uc5b4, 216 = 6 * 6 * 6 = 8 * 27\uc774\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc22b\uc790\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc18c\uc778\uc218\ub97c \ubaa8\ub450 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\r\n\t\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, \uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc218\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774 \uc218\ub294 1\ubcf4\ub2e4 \ud06c\uace0, 300000\ubcf4\ub2e4 \uc791\ub2e4. \uc785\ub825\uc758 \ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 1\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\r\n\t\uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4 \uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc22b\uc790\uc5d0 \ub300\ud574\uc11c, \uadf8 \uc22b\uc790\ub97c \ucd9c\ub825\ud558\uace0, &quot;:&quot;\uc744 \ucd9c\ub825\ud55c \ub2e4\uc74c\uc5d0 \uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc18c\uc778\uc218\ub97c \uc624\ub984\ucc28\uc21c\uc73c\ub85c \ucd9c\ub825\ud55c\ub2e4. \ubaa8\ub4e0 \uc6d4\uc694\uc77c-\ud1a0\uc694\uc77c \uc18c\uc778\uc218 \uc55e\uc5d0\ub294 \uacf5\ubc31\uc744 \ud55c \uce78 \ucd9c\ub825\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"4969","problem_lang":"1","title":"Monday-Saturday Prime Factors","description":"<p>Chief Judge&#39;s log, stardate 48642.5. We have decided to make a problem from elementary number theory. The problem looks like finding all prime factors of a positive integer, but it is not.<\/p>\r\n\r\n<p>A positive integer whose remainder divided by 7 is either 1 or 6 is called a 7N+{1,6} number. But as it is hard to pronounce, we shall call it a Monday-Saturday number.<\/p>\r\n\r\n<p>For Monday-Saturday numbers a and b, we say a is a Monday-Saturday divisor of b if there exists a Monday-Saturday number x such that ax = b. It is easy to show that for any Monday-Saturday numbers a and b, it holds that a is a Monday-Saturday divisor of b if and only if a is a divisor of b in the usual sense.<\/p>\r\n\r\n<p>We call a Monday-Saturday number a Monday-Saturday prime if it is greater than 1 and has no Monday-Saturday divisors other than itself and 1. A Monday-Saturday number which is a prime in the usual sense is a Monday-Saturday prime but the converse does not always hold. For example, 27 is a Monday-Saturday prime although it is not a prime in the usual sense. We call a Monday-Saturday prime which is a Monday-Saturday divisor of a Monday-Saturday number a a Monday-Saturday prime factor of a. For example, 27 is one of the Monday-Saturday prime factors of 216, since 27 is a Monday-Saturday prime and 216 = 27 &times; 8 holds.<\/p>\r\n\r\n<p>Any Monday-Saturday number greater than 1 can be expressed as a product of one or more Monday-Saturday primes. The expression is not always unique even if differences in order are ignored. For example, 216 = 6 &times; 6 &times; 6 = 8 &times; 27 holds.<\/p>\r\n\r\n<p>Our contestants should write a program that outputs all Monday-Saturday prime factors of each input Monday-Saturday number.<\/p>\r\n","input":"<p>The input is a sequence of lines each of which contains a single Monday-Saturday number. Each Monday-Saturday number is greater than 1 and less than 300000 (three hundred thousand). The end of the input is indicated by a line containing a single digit 1.<\/p>\r\n","output":"<p>For each input Monday-Saturday number, it should be printed, followed by a colon `:&#39; and the list of its Monday-Saturday prime factors on a single line. Monday-Saturday prime factors should be listed in ascending order and each should be preceded by a space. All the Monday-Saturday prime factors should be printed only once even if they divide the input Monday-Saturday number more than once.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]