시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
5 초 512 MB 4 1 1 50.000%

문제

"Divisor is the Conquerer"은 혼자 할 수 있는 카드 게임이다. 보통 이런 단순한 게임은 시간을 보내기 좋은 방법이지만, 프로그래머인 당신은 그 시간에 프로그래밍을 하고 싶을 것이다. 당신의 과제는 "Divisor is the Conquerer" 게임을 자동으로 해결하는 컴퓨터 프로그램을 만드는 것이다. 아래에 게임 규칙이 있다.

먼저, 무작위로 N개의 카드를 카드 덱에서 뽑는다 (1 ≤ N ≤ 52). 게임은 뽑은 카드들만을 이용해서 진행되고, 다른 카드들은 사용되지 않을 것이다.

그뒤 반복해서 한 장씩 카드를 바닥에 내려놓는다. 맨 처음 내려놓을 때는 어떤 카드이든 내려놓을 수 있다. 그 뒤에는 내려놓은 카드들을 "지배하는" 카드만을 내려놓을 수 있다. 어떤 카드가 카드들의 집합을 지배한다는 것은 카드가 의미하는 수가 카드 집합의 수들의 합을 나눈다는 것이다. 예를 들어, 카드 7은 집합 {5, 11, 12}를 지배하지만, 카드 11은 집합 {5, 7, 12}를 지배하지 않는다. 

처음에 고른 N개의 카드를 모두 내려놓으면 게임에 승리하게 된다. 이것에 실패하면, 즉 중간에 카드를 내려놓을 수 없게 되면 패배한 것이다.

입력

입력은 여러 개의 테스트 케이트로 구성된다.

각 테스트 케이스는 두 줄로 이루어진다. 첫번째 줄에는 카드의 개수를 의미하는 정수 N (1 ≤ N ≤ 52) 이 있다. 두번째 줄은 각 카드가 의미하는 숫자를 뜻하는 N개의 정수  c, . . . , cN (1 ≤ ci ≤ 13) 로 구성된다. 한 테스트 케이스에서 같은 수를 의미하는 카드의 개수가 최대 4개까지라는 것을 가정해도 된다.

0이 입력되면 입력이 끝난다.

출력

각각의 테스트 케이스에 대해 한 줄씩 출력한다. 입력된 초기 조건에서 이길 수 있는 전략이 있으면, 가능한 전략 중 아무거나 N개짜리 정수 목록으로 공백으로 구분하여 출력한다.

만약 이길 수 있는 방법이 없으면, “No”라고 출력한다.

예제 입력 1

5
1 2 3 3 7
4
2 3 3 3
0

예제 출력 1

3 3 1 7 2
No
[{"problem_id":"13848","problem_lang":"0","title":"\ub098\ub204\ub294 \uc790\uac00 \uc9c0\ubc30\ud55c\ub2e4","description":"<p>&quot;Divisor is the Conquerer&quot;\uc740 \ud63c\uc790 \ud560 \uc218 \uc788\ub294 \uce74\ub4dc \uac8c\uc784\uc774\ub2e4. \ubcf4\ud1b5 \uc774\ub7f0 \ub2e8\uc21c\ud55c \uac8c\uc784\uc740 \uc2dc\uac04\uc744 \ubcf4\ub0b4\uae30 \uc88b\uc740 \ubc29\ubc95\uc774\uc9c0\ub9cc, \ud504\ub85c\uadf8\ub798\uba38\uc778 \ub2f9\uc2e0\uc740 \uadf8 \uc2dc\uac04\uc5d0 \ud504\ub85c\uadf8\ub798\ubc0d\uc744 \ud558\uace0 \uc2f6\uc744 \uac83\uc774\ub2e4. \ub2f9\uc2e0\uc758 \uacfc\uc81c\ub294&nbsp;&quot;Divisor is the Conquerer&quot; \uac8c\uc784\uc744 \uc790\ub3d9\uc73c\ub85c \ud574\uacb0\ud558\ub294 \ucef4\ud4e8\ud130 \ud504\ub85c\uadf8\ub7a8\uc744 \ub9cc\ub4dc\ub294 \uac83\uc774\ub2e4. \uc544\ub798\uc5d0 \uac8c\uc784 \uaddc\uce59\uc774 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uba3c\uc800, \ubb34\uc791\uc704\ub85c N\uac1c\uc758 \uce74\ub4dc\ub97c \uce74\ub4dc \ub371\uc5d0\uc11c \ubf51\ub294\ub2e4&nbsp;(1 &le; N &le; 52). \uac8c\uc784\uc740 \ubf51\uc740 \uce74\ub4dc\ub4e4\ub9cc\uc744 \uc774\uc6a9\ud574\uc11c \uc9c4\ud589\ub418\uace0, \ub2e4\ub978 \uce74\ub4dc\ub4e4\uc740 \uc0ac\uc6a9\ub418\uc9c0 \uc54a\uc744 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>\uadf8\ub4a4 \ubc18\ubcf5\ud574\uc11c \ud55c \uc7a5\uc529 \uce74\ub4dc\ub97c \ubc14\ub2e5\uc5d0 \ub0b4\ub824\ub193\ub294\ub2e4. \ub9e8 \ucc98\uc74c \ub0b4\ub824\ub193\uc744 \ub54c\ub294 \uc5b4\ub5a4 \uce74\ub4dc\uc774\ub4e0 \ub0b4\ub824\ub193\uc744 \uc218 \uc788\ub2e4. \uadf8 \ub4a4\uc5d0\ub294 \ub0b4\ub824\ub193\uc740 \uce74\ub4dc\ub4e4\uc744 &quot;\uc9c0\ubc30\ud558\ub294&quot; \uce74\ub4dc\ub9cc\uc744 \ub0b4\ub824\ub193\uc744 \uc218 \uc788\ub2e4. \uc5b4\ub5a4 \uce74\ub4dc\uac00 \uce74\ub4dc\ub4e4\uc758 \uc9d1\ud569\uc744 \uc9c0\ubc30\ud55c\ub2e4\ub294 \uac83\uc740 \uce74\ub4dc\uac00 \uc758\ubbf8\ud558\ub294 \uc218\uac00 \uce74\ub4dc \uc9d1\ud569\uc758 \uc218\ub4e4\uc758 \ud569\uc744 \ub098\ub208\ub2e4\ub294 \uac83\uc774\ub2e4. \uc608\ub97c \ub4e4\uc5b4, \uce74\ub4dc 7\uc740 \uc9d1\ud569 {5, 11, 12}\ub97c \uc9c0\ubc30\ud558\uc9c0\ub9cc, \uce74\ub4dc 11\uc740 \uc9d1\ud569 {5, 7, 12}\ub97c \uc9c0\ubc30\ud558\uc9c0 \uc54a\ub294\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\ucc98\uc74c\uc5d0 \uace0\ub978 N\uac1c\uc758 \uce74\ub4dc\ub97c \ubaa8\ub450 \ub0b4\ub824\ub193\uc73c\uba74 \uac8c\uc784\uc5d0 \uc2b9\ub9ac\ud558\uac8c \ub41c\ub2e4. \uc774\uac83\uc5d0 \uc2e4\ud328\ud558\uba74, \uc989 \uc911\uac04\uc5d0 \uce74\ub4dc\ub97c \ub0b4\ub824\ub193\uc744 \uc218 \uc5c6\uac8c \ub418\uba74 \ud328\ubc30\ud55c \uac83\uc774\ub2e4.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \uc5ec\ub7ec \uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\ud2b8\ub85c \uad6c\uc131\ub41c\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \ub450 \uc904\ub85c \uc774\ub8e8\uc5b4\uc9c4\ub2e4. \uccab\ubc88\uc9f8 \uc904\uc5d0\ub294 \uce74\ub4dc\uc758 \uac1c\uc218\ub97c \uc758\ubbf8\ud558\ub294 \uc815\uc218 N&nbsp;(1 &le; N &le; 52) \uc774 \uc788\ub2e4. \ub450\ubc88\uc9f8 \uc904\uc740 \uac01 \uce74\ub4dc\uac00 \uc758\ubbf8\ud558\ub294 \uc22b\uc790\ub97c \ub73b\ud558\ub294 N\uac1c\uc758 \uc815\uc218&nbsp;&nbsp;c<sub>1&nbsp;<\/sub>, . . . , c<sub>N<\/sub> (1 &le; c<sub>i<\/sub> &le; 13) \ub85c \uad6c\uc131\ub41c\ub2e4. \ud55c \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0\uc11c \uac19\uc740 \uc218\ub97c \uc758\ubbf8\ud558\ub294 \uce74\ub4dc\uc758 \uac1c\uc218\uac00 \ucd5c\ub300 4\uac1c\uae4c\uc9c0\ub77c\ub294 \uac83\uc744 \uac00\uc815\ud574\ub3c4 \ub41c\ub2e4.<\/p>\r\n\r\n<p>0\uc774 \uc785\ub825\ub418\uba74 \uc785\ub825\uc774 \ub05d\ub09c\ub2e4.<\/p>\r\n","output":"<p>\uac01\uac01\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574 \ud55c \uc904\uc529 \ucd9c\ub825\ud55c\ub2e4. \uc785\ub825\ub41c \ucd08\uae30 \uc870\uac74\uc5d0\uc11c \uc774\uae38 \uc218 \uc788\ub294 \uc804\ub7b5\uc774 \uc788\uc73c\uba74, \uac00\ub2a5\ud55c \uc804\ub7b5 \uc911 \uc544\ubb34\uac70\ub098 N\uac1c\uc9dc\ub9ac \uc815\uc218 \ubaa9\ub85d\uc73c\ub85c \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ud558\uc5ec \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub9cc\uc57d \uc774\uae38 \uc218 \uc788\ub294 \ubc29\ubc95\uc774 \uc5c6\uc73c\uba74,&nbsp;&ldquo;No&rdquo;\ub77c\uace0 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"13848","problem_lang":"1","title":"Divisor is the Conqueror","description":"<p>Divisor is the Conquerer is a solitaire card game. Although this simple game itself is a great way to pass one&rsquo;s time, you, a programmer, always kill your time by programming. Your task is to write a computer program that automatically solves Divisor is the Conquerer games. Here is the rule of this game:<\/p>\r\n\r\n<p>First, you randomly draw N cards (1 &le; N &le; 52) from your deck of playing cards. The game is played only with those cards; the other cards will not be used.<\/p>\r\n\r\n<p>Then you repeatedly pick one card to play among those in your hand. You are allowed to choose any card in the initial turn. After that, you are only allowed to pick a card that conquers the cards you have already played. A card is said to conquer a set of cards when the rank of the card divides the sum of the ranks in the set. For example, the card 7 conquers the set {5, 11, 12}, while the card 11 does not conquer the set {5, 7, 12}.<\/p>\r\n\r\n<p>You win the game if you successfully play all N cards you have drawn. You lose if you fails, that is, you faces a situation in which no card in your hand conquers the set of cards you have played.<\/p>\r\n","input":"<p>The input consists of multiple test cases.<\/p>\r\n\r\n<p>Each test case consists of two lines. The first line contains an integer N (1 &le; N &le; 52), which represents the number of the cards. The second line contains N integers c<sub>1<\/sub>, . . . , c<sub>N<\/sub> (1 &le; c<sub>i<\/sub> &le; 13), each of which represents the rank of the card. You may assume that there are at most four cards with the same rank in one list.<\/p>\r\n\r\n<p>The input is terminated by a line with a single zero.<\/p>\r\n","output":"<p>For each test case, you should output one line. If there are any winning strategies for the cards of the input, print any one of them as a list of N integers separated by a space.<\/p>\r\n\r\n<p>If there is no winning strategy, print &ldquo;No&rdquo;.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]