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문제

전설적인 인천 식료품가게의 주인인 김인천 씨는 대대적인 할인행사를 계획하고 있습니다. 계산을 단순하게하기 위해 그는 25% 할인된 가격으로 상점의 모든 품목을 판매하기로 결정했습니다. 즉, 각 품목의 판매 가격은 정상 가격의 정확히 75 %입니다. 우연하게도 인천 식료품가게에서 판매하는 모든 물건의 정상가는 4의 배수인 정수이고, 할인된 가격 역시 편리하게도 모두 정수입니다.

김인천씨는 이 할인행사를 준비하기위해서 먼저 모든 판매물품의 할인된 판매가격을 프린터로 출력을 실행했고, 또한 할인행사 종료후 다시 쓸 모든 품목에 정상가격표 역시 출력을 실행하였습니다.

손님이 찾아와 잠깐 자리를 비웠던 김인천씨가 다시 가격표의 출력을 확인하기 위해서 프린터로 돌아와보니, 공교롭게 프린터는 모든 물품의 할인가격과 정상가격을 따로 구분하지 않고 오름차순으로 정렬한 뒤 순서대로 출력하여 하나의 출력물 더미를 만들었습니다. 각 품목의 할인가격표와 정상가격표 모두가 출력물 더미의 어딘가에 있습니다. 그러나 두 유형(할인가격, 정상가격)의 가격표는 비슷하게 보이고, 모든 품목의 가격을 기억하지 못하기 때문에 김인천씨는 어느 가격표가 할인가격표인지 확신할 수 없습니다. 이 상황에서 김인천씨는 무엇이 할인가격표인지 구분해낼 수 있을까요?

예를 들어, 정상가격이 20, 80, 100 인 경우 할인가격은 15, 60, 75이며 프린터의 인쇄출력더미는 오름차순으로 정렬된 15, 20, 60, 75, 80, 100 가격표들로 구성됩니다.

입력

입력의 첫 번째 라인(줄)은 테스트 사례의 케이스의 수 T를 나타냅니다. 이후의 라인은 T개의 테스트 케이스가 이어집니다. 각 테스트 케이스는 두 줄로 구성됩니다. 첫 번째 줄에는 INU 식료품가게에 존재하는 상품수인 단일 정수 N이 포함됩니다. 두 번째 줄에는 프린터에서 가격의 오름차순으로 인쇄한 2N개의 정수 P1, P2, ..., P2N이 주어집니다.

입력값의 제한은 아래와 같습니다

  • 1 ≤ T ≤ 100.
  • 모든 i에 대해서 1 ≤ Pi ≤ 109.
  • 모든 i에 대해서 Pi ≤ Pi+1. (가격은 오름차순으로 존재)
  • 정답은 단 하나만 존재하는것이 보장되어 있음.
  • 1 ≤ N ≤ 4.
     

출력

개별 테스트 케이스에 대해서 출력라인은 “Case #x: y” 형식(큰 따옴표는 제외)으로 출력하며,  x는 1부터 시작하는 테스트 케이스의 번호 (인덱스)이며, y는 할인가격에 해당하는 오름차순으로 정렬된 N개의 정수들이다.

예제 입력 1

2
3
15 20 60 75 80 100
4
9 9 12 12 12 15 16 20

예제 출력 1

Case #1: 15 60 75
Case #2: 9 9 12 15

힌트

예제의 첫 번째 테스트 케이스인 Case #1은 문제에서 예로들어서 설명한 세 개의 물품에 대한 정상가격과 할인가격 6개입니다. 또한 예제의 Case #2에서는 여러 품목이 동일한 가격을 가질 수 있고, 어떤 품목의 할인가격이 다른 품목 정상가격과 같을 수도 있습니다.

[{"problem_id":"12033","problem_lang":"0","title":"\uae40\uc778\ucc9c\uc528\uc758 \uc2dd\ub8cc\ud488\uac00\uac8c (Small)","description":"<p dir=\"ltr\">\uc804\uc124\uc801\uc778 \uc778\ucc9c \uc2dd\ub8cc\ud488\uac00\uac8c\uc758 \uc8fc\uc778\uc778 \uae40\uc778\ucc9c \uc528\ub294 \ub300\ub300\uc801\uc778 \ud560\uc778\ud589\uc0ac\ub97c \uacc4\ud68d\ud558\uace0 \uc788\uc2b5\ub2c8\ub2e4. \uacc4\uc0b0\uc744 \ub2e8\uc21c\ud558\uac8c\ud558\uae30 \uc704\ud574 \uadf8\ub294 25% \ud560\uc778\ub41c \uac00\uaca9\uc73c\ub85c \uc0c1\uc810\uc758 \ubaa8\ub4e0 \ud488\ubaa9\uc744 \ud310\ub9e4\ud558\uae30\ub85c \uacb0\uc815\ud588\uc2b5\ub2c8\ub2e4. \uc989, \uac01 \ud488\ubaa9\uc758 \ud310\ub9e4 \uac00\uaca9\uc740 \uc815\uc0c1 \uac00\uaca9\uc758 \uc815\ud655\ud788 75 %\uc785\ub2c8\ub2e4. \uc6b0\uc5f0\ud558\uac8c\ub3c4 \uc778\ucc9c \uc2dd\ub8cc\ud488\uac00\uac8c\uc5d0\uc11c \ud310\ub9e4\ud558\ub294 \ubaa8\ub4e0 \ubb3c\uac74\uc758 \uc815\uc0c1\uac00\ub294 4\uc758 \ubc30\uc218\uc778 \uc815\uc218\uc774\uace0, \ud560\uc778\ub41c \uac00\uaca9 \uc5ed\uc2dc \ud3b8\ub9ac\ud558\uac8c\ub3c4 \ubaa8\ub450 \uc815\uc218\uc785\ub2c8\ub2e4.<\/p>\r\n\r\n<p dir=\"ltr\">\uae40\uc778\ucc9c\uc528\ub294 \uc774 \ud560\uc778\ud589\uc0ac\ub97c \uc900\ube44\ud558\uae30\uc704\ud574\uc11c \uba3c\uc800 \ubaa8\ub4e0 \ud310\ub9e4\ubb3c\ud488\uc758 \ud560\uc778\ub41c \ud310\ub9e4\uac00\uaca9\uc744 \ud504\ub9b0\ud130\ub85c \ucd9c\ub825\uc744 \uc2e4\ud589\ud588\uace0, \ub610\ud55c \ud560\uc778\ud589\uc0ac \uc885\ub8cc\ud6c4 \ub2e4\uc2dc \uc4f8 \ubaa8\ub4e0 \ud488\ubaa9\uc5d0 \uc815\uc0c1\uac00\uaca9\ud45c \uc5ed\uc2dc \ucd9c\ub825\uc744 \uc2e4\ud589\ud558\uc600\uc2b5\ub2c8\ub2e4.<\/p>\r\n\r\n<p dir=\"ltr\">\uc190\ub2d8\uc774 \ucc3e\uc544\uc640 \uc7a0\uae50 \uc790\ub9ac\ub97c \ube44\uc6e0\ub358 \uae40\uc778\ucc9c\uc528\uac00 \ub2e4\uc2dc \uac00\uaca9\ud45c\uc758 \ucd9c\ub825\uc744 \ud655\uc778\ud558\uae30 \uc704\ud574\uc11c \ud504\ub9b0\ud130\ub85c \ub3cc\uc544\uc640\ubcf4\ub2c8, \uacf5\uad50\ub86d\uac8c \ud504\ub9b0\ud130\ub294 \ubaa8\ub4e0 \ubb3c\ud488\uc758 \ud560\uc778\uac00\uaca9\uacfc \uc815\uc0c1\uac00\uaca9\uc744 \ub530\ub85c \uad6c\ubd84\ud558\uc9c0 \uc54a\uace0 \uc624\ub984\ucc28\uc21c\uc73c\ub85c \uc815\ub82c\ud55c \ub4a4 \uc21c\uc11c\ub300\ub85c \ucd9c\ub825\ud558\uc5ec \ud558\ub098\uc758 \ucd9c\ub825\ubb3c \ub354\ubbf8\ub97c \ub9cc\ub4e4\uc5c8\uc2b5\ub2c8\ub2e4. \uac01 \ud488\ubaa9\uc758 \ud560\uc778\uac00\uaca9\ud45c\uc640 \uc815\uc0c1\uac00\uaca9\ud45c \ubaa8\ub450\uac00 \ucd9c\ub825\ubb3c \ub354\ubbf8\uc758 \uc5b4\ub518\uac00\uc5d0 \uc788\uc2b5\ub2c8\ub2e4. \uadf8\ub7ec\ub098 \ub450 \uc720\ud615(\ud560\uc778\uac00\uaca9, \uc815\uc0c1\uac00\uaca9)\uc758 \uac00\uaca9\ud45c\ub294 \ube44\uc2b7\ud558\uac8c \ubcf4\uc774\uace0, \ubaa8\ub4e0 \ud488\ubaa9\uc758 \uac00\uaca9\uc744 \uae30\uc5b5\ud558\uc9c0 \ubabb\ud558\uae30 \ub54c\ubb38\uc5d0 \uae40\uc778\ucc9c\uc528\ub294 \uc5b4\ub290 \uac00\uaca9\ud45c\uac00 \ud560\uc778\uac00\uaca9\ud45c\uc778\uc9c0 \ud655\uc2e0\ud560 \uc218 \uc5c6\uc2b5\ub2c8\ub2e4. \uc774 \uc0c1\ud669\uc5d0\uc11c \uae40\uc778\ucc9c\uc528\ub294 \ubb34\uc5c7\uc774 \ud560\uc778\uac00\uaca9\ud45c\uc778\uc9c0 \uad6c\ubd84\ud574\ub0bc \uc218 \uc788\uc744\uae4c\uc694?<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, \uc815\uc0c1\uac00\uaca9\uc774 20, 80, 100 \uc778 \uacbd\uc6b0 \ud560\uc778\uac00\uaca9\uc740 15, 60, 75\uc774\uba70 \ud504\ub9b0\ud130\uc758 \uc778\uc1c4\ucd9c\ub825\ub354\ubbf8\ub294 \uc624\ub984\ucc28\uc21c\uc73c\ub85c \uc815\ub82c\ub41c 15, 20, 60, 75, 80, 100 \uac00\uaca9\ud45c\ub4e4\ub85c \uad6c\uc131\ub429\ub2c8\ub2e4.<\/p>\r\n","input":"<p dir=\"ltr\">\uc785\ub825\uc758 \uccab \ubc88\uc9f8 \ub77c\uc778(\uc904)\uc740 \ud14c\uc2a4\ud2b8 \uc0ac\ub840\uc758 \ucf00\uc774\uc2a4\uc758 \uc218 T\ub97c \ub098\ud0c0\ub0c5\ub2c8\ub2e4. \uc774\ud6c4\uc758 \ub77c\uc778\uc740 T\uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uac00 \uc774\uc5b4\uc9d1\ub2c8\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \ub450 \uc904\ub85c \uad6c\uc131\ub429\ub2c8\ub2e4. \uccab \ubc88\uc9f8 \uc904\uc5d0\ub294 INU \uc2dd\ub8cc\ud488\uac00\uac8c\uc5d0 \uc874\uc7ac\ud558\ub294 \uc0c1\ud488\uc218\uc778 \ub2e8\uc77c \uc815\uc218 N\uc774 \ud3ec\ud568\ub429\ub2c8\ub2e4. \ub450 \ubc88\uc9f8 \uc904\uc5d0\ub294 \ud504\ub9b0\ud130\uc5d0\uc11c \uac00\uaca9\uc758 \uc624\ub984\ucc28\uc21c\uc73c\ub85c \uc778\uc1c4\ud55c 2N\uac1c\uc758 \uc815\uc218 P1, P2, ..., P2N\uc774 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4.<\/p>\r\n\r\n<p dir=\"ltr\">\uc785\ub825\uac12\uc758 \uc81c\ud55c\uc740 \uc544\ub798\uc640 \uac19\uc2b5\ub2c8\ub2e4<\/p>\r\n\r\n<ul dir=\"ltr\">\r\n\t<li>1 &le; T &le; 100.<\/li>\r\n\t<li>\ubaa8\ub4e0 i\uc5d0 \ub300\ud574\uc11c 1 &le; P<sub>i<\/sub> &le; 10<sup>9<\/sup>.<\/li>\r\n\t<li>\ubaa8\ub4e0 i\uc5d0 \ub300\ud574\uc11c P<sub>i<\/sub> &le; P<sub>i+1<\/sub>. (\uac00\uaca9\uc740 \uc624\ub984\ucc28\uc21c\uc73c\ub85c \uc874\uc7ac)<\/li>\r\n\t<li>\uc815\ub2f5\uc740 \ub2e8 \ud558\ub098\ub9cc \uc874\uc7ac\ud558\ub294\uac83\uc774 \ubcf4\uc7a5\ub418\uc5b4 \uc788\uc74c.<\/li>\r\n\t<li>1 &le; N &le; 4.<br \/>\r\n\t&nbsp;<\/li>\r\n<\/ul>\r\n","output":"<p dir=\"ltr\">\uac1c\ubcc4 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574\uc11c \ucd9c\ub825\ub77c\uc778\uc740 &ldquo;Case #x: y&rdquo; \ud615\uc2dd(\ud070 \ub530\uc634\ud45c\ub294 \uc81c\uc678)\uc73c\ub85c \ucd9c\ub825\ud558\uba70, &nbsp;x\ub294 1\ubd80\ud130 \uc2dc\uc791\ud558\ub294 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \ubc88\ud638 (\uc778\ub371\uc2a4)\uc774\uba70, y\ub294 \ud560\uc778\uac00\uaca9\uc5d0 \ud574\ub2f9\ud558\ub294 \uc624\ub984\ucc28\uc21c\uc73c\ub85c \uc815\ub82c\ub41c N\uac1c\uc758 \uc815\uc218\ub4e4\uc774\ub2e4.<\/p>\r\n","hint":"<p dir=\"ltr\">\uc608\uc81c\uc758 \uccab \ubc88\uc9f8 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc778 Case #1\uc740 \ubb38\uc81c\uc5d0\uc11c \uc608\ub85c\ub4e4\uc5b4\uc11c \uc124\uba85\ud55c \uc138 \uac1c\uc758 \ubb3c\ud488\uc5d0 \ub300\ud55c \uc815\uc0c1\uac00\uaca9\uacfc \ud560\uc778\uac00\uaca9 6\uac1c\uc785\ub2c8\ub2e4. \ub610\ud55c \uc608\uc81c\uc758 Case #2\uc5d0\uc11c\ub294 \uc5ec\ub7ec \ud488\ubaa9\uc774 \ub3d9\uc77c\ud55c \uac00\uaca9\uc744 \uac00\uc9c8 \uc218 \uc788\uace0, \uc5b4\ub5a4 \ud488\ubaa9\uc758 \ud560\uc778\uac00\uaca9\uc774 \ub2e4\ub978 \ud488\ubaa9 \uc815\uc0c1\uac00\uaca9\uacfc \uac19\uc744 \uc218\ub3c4 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"12033","problem_lang":"1","title":"Cody's Jams (Small)","description":"<p>Cody, the owner of the legendary Cody&#39;s Jams store, is planning a huge jam sale. To make things simple, he has decided to sell every item in his store at a 25% discount &mdash; that is, each item&#39;s sale price is exactly 75% of its regular price. Since all of his regular prices happened to be integers divisible by four, his sale prices are conveniently also all integers.<\/p>\r\n\r\n<p>To prepare for the sale, he placed an order to print new labels for all of his items at their sale prices. He also placed an order to print new labels for all of his items at their regular prices, to use once the sale is over.<\/p>\r\n\r\n<p>Cody just came back from picking up his order. Unfortunately, the printer gave him both orders in one combined stack, sorted by price. Both the sale price and the regular price label for each item are present somewhere in the stack. However, both types of labels look the same, and since he does not remember the price of every item, he is not sure which labels are the sale price labels. Can you figure that out?<\/p>\r\n\r\n<p>For instance, if the regular prices were 20, 80, and 100, the sale prices would be 15, 60, and 75, and the printer&#39;s stack would consist of the labels 15, 20, 60, 75, 80, and 100.<\/p>\r\n","input":"<p>The first line of the input gives the number of test cases,&nbsp;<strong>T<\/strong>.&nbsp;<strong>T<\/strong>&nbsp;test cases follow. Each test case consists of two lines. The first line contains a single integer&nbsp;<strong>N<\/strong>, the number of items in Cody&#39;s store. The second line contains 2<strong>N<\/strong>&nbsp;integers&nbsp;<strong>P<sub>1<\/sub><\/strong>,&nbsp;<strong>P<sub>2<\/sub><\/strong>, ...,&nbsp;<strong>P<sub>2N<\/sub><\/strong>&nbsp;in non-decreasing order by the price printed on each label given by the printer.<\/p>\r\n\r\n<p>Limit<\/p>\r\n\r\n<ul>\r\n\t<li>1 &le;&nbsp;<strong>T<\/strong>&nbsp;&le; 100.<\/li>\r\n\t<li>1 &le;&nbsp;<strong>P<sub>i<\/sub><\/strong>&nbsp;&le; 10<sup>9<\/sup>, for all i.<\/li>\r\n\t<li><strong>P<sub>i<\/sub><\/strong>&nbsp;&le;&nbsp;<strong>P<sub>i+1<\/sub><\/strong>, for all i. (The prices are in non-decreasing order.)<\/li>\r\n\t<li>It is guaranteed that a unique solution exists.<\/li>\r\n\t<li>1 &le;&nbsp;<strong>N<\/strong>&nbsp;&le; 4.<\/li>\r\n<\/ul>\r\n","output":"<p>For each test case, output one line containing&nbsp;<code>Case #x: y<\/code>, where&nbsp;<code>x<\/code>&nbsp;is the test case number (starting from 1) and&nbsp;<code>y<\/code>&nbsp;is a list of&nbsp;<strong>N<\/strong>&nbsp;integers: the labels containing sale prices, in non-decreasing order.<\/p>\r\n","hint":"<p>Case #1 is the one described in the problem statement.<\/p>\r\n\r\n<p>Notice in Case #2 that it is possible for multiple items to have the same price, and for an item to have a regular price that equals the sale price of another item.<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"English"}]

채점 및 기타 정보

  • 예제는 채점하지 않는다.