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문제

블리트릭스라는 양은 더 빨리 잠을 들기 위한 전략을 세웠다.

먼저, 숫자 N을 뽑는다. 그리고 N, 2 × N, 3 × N 등을 떠올린다. 숫자를 떠올릴 때 마다, 그 숫자의 모든 자리수의 숫자들을 적어놓는데, 이미 적은 숫자는 또 적지 않는다. 0에서 9까지의 모든 숫자가 적히게 되면 잠이 든다.

블리트릭스는 N에서 시작해서 i × N 후에는 (i + 1) × N을 떠올리게 된다. 예를 들어 N = 1692 일 경우, 다음 과 같이 진행된다:

  • N = 1692. 1, 2, 6, 9가 기록된다.
  • 2N = 3384. 1, 2, 3, 4, 6, 8, 9가 기록된다.
  • 3N = 5076. 모든 수가 기록되고, 잠에 빠진다.

블리트릭스가 잠에 빠지는 수는 무엇인가? 영원히 잠에 들 수 없다면 INSOMNIA라고 출력하라.

입력

첫 번째 행은 케이스의 개수, T이다. 다음 행부터는 T개의 케이스들이 나온다. 각 케이스는 블리트릭스가 고른 하나의 숫자 N으로 구성된다.

제한

  • 1 ≤ T ≤ 100.
  • 0 ≤ N ≤ 106.

출력

각 케이스에 대해서, 케이스 번호가 x이고 y가 정답일 때, Case #x: y라고 출력해야 한다.

예제 입력 1

5
0
1
2
11
1692

예제 출력 1

Case #1: INSOMNIA
Case #2: 10
Case #3: 90
Case #4: 110
Case #5: 5076

힌트

예제 입출력 1번에 대해서, 2 × 0 = 0, 3 × 0 = 0 등등으로 이어지므로, 블리트릭스는 0외에는 다른 숫자를 기록할 수 없을 것이며, 따라서 영원히 잠에 들 수 없다.

예제 입출력 2번의 경우, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 순으로 떠올릴 것이며, 0이 가장 마지막에 기록되는 수가 될 것이다. 따라서 10이 마지막 수가 될 것이다.

예제 입출력 3번의 경우, 2, 4, 6... 등등으로 떠올릴 것이다. 숫자 9는 90 전에는 기록할 수 없다. 90을 떠올렸을 때 이미 블리트릭스는 0~8의 숫자를 적었을 것이므로, 90이 마지막 수가 될 것이다.

예제 입출력 4번은 블리트릭스가 11, 22, 33, 44, 55, 66, 77, 88, 99, 110 을 떠올릴 것이고, 110이 마지막 수가 될 것이다.

예제 입출력 5번은 문제에서 설명한 수이다.

[{"problem_id":"14382","problem_lang":"0","title":"\uc22b\uc790\uc138\ub294 \uc591 (Large)","description":"<p dir=\"ltr\">\ube14\ub9ac\ud2b8\ub9ad\uc2a4\ub77c\ub294 \uc591\uc740 \ub354 \ube68\ub9ac \uc7a0\uc744 \ub4e4\uae30 \uc704\ud55c \uc804\ub7b5\uc744 \uc138\uc6e0\ub2e4.<\/p>\r\n\r\n<p dir=\"ltr\">\uba3c\uc800, \uc22b\uc790 N\uc744 \ubf51\ub294\ub2e4. \uadf8\ub9ac\uace0 N, 2 &times; N, 3 &times; N \ub4f1\uc744 \ub5a0\uc62c\ub9b0\ub2e4. \uc22b\uc790\ub97c \ub5a0\uc62c\ub9b4 \ub54c \ub9c8\ub2e4, \uadf8 \uc22b\uc790\uc758 \ubaa8\ub4e0 \uc790\ub9ac\uc218\uc758 \uc22b\uc790\ub4e4\uc744 \uc801\uc5b4\ub193\ub294\ub370, \uc774\ubbf8 \uc801\uc740 \uc22b\uc790\ub294 \ub610 \uc801\uc9c0 \uc54a\ub294\ub2e4. 0\uc5d0\uc11c 9\uae4c\uc9c0\uc758 \ubaa8\ub4e0 \uc22b\uc790\uac00 \uc801\ud788\uac8c \ub418\uba74 \uc7a0\uc774 \ub4e0\ub2e4.<\/p>\r\n\r\n<p dir=\"ltr\">\ube14\ub9ac\ud2b8\ub9ad\uc2a4\ub294 N\uc5d0\uc11c \uc2dc\uc791\ud574\uc11c i &times; N \ud6c4\uc5d0\ub294 (i + 1) &times; N\uc744 \ub5a0\uc62c\ub9ac\uac8c \ub41c\ub2e4. \uc608\ub97c \ub4e4\uc5b4 N = 1692 \uc77c \uacbd\uc6b0, \ub2e4\uc74c \uacfc \uac19\uc774 \uc9c4\ud589\ub41c\ub2e4:<\/p>\r\n\r\n<ul>\r\n\t<li dir=\"ltr\">N = 1692. 1, 2, 6, 9\uac00 \uae30\ub85d\ub41c\ub2e4.<\/li>\r\n\t<li dir=\"ltr\">2N = 3384. 1, 2, 3, 4, 6, 8, 9\uac00 \uae30\ub85d\ub41c\ub2e4.<\/li>\r\n\t<li dir=\"ltr\">3N = 5076. \ubaa8\ub4e0 \uc218\uac00 \uae30\ub85d\ub418\uace0, \uc7a0\uc5d0 \ube60\uc9c4\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\ube14\ub9ac\ud2b8\ub9ad\uc2a4\uac00 \uc7a0\uc5d0 \ube60\uc9c0\ub294 \uc218\ub294 \ubb34\uc5c7\uc778\uac00? \uc601\uc6d0\ud788 \uc7a0\uc5d0 \ub4e4 \uc218 \uc5c6\ub2e4\uba74 INSOMNIA\ub77c\uace0 \ucd9c\ub825\ud558\ub77c.<\/p>\r\n","input":"<p dir=\"ltr\">\uccab \ubc88\uc9f8 \ud589\uc740 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218, T\uc774\ub2e4. \ub2e4\uc74c \ud589\ubd80\ud130\ub294 T\uac1c\uc758 \ucf00\uc774\uc2a4\ub4e4\uc774 \ub098\uc628\ub2e4. \uac01 \ucf00\uc774\uc2a4\ub294 \ube14\ub9ac\ud2b8\ub9ad\uc2a4\uac00 \uace0\ub978 \ud558\ub098\uc758 \uc22b\uc790 N\uc73c\ub85c \uad6c\uc131\ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc81c\ud55c<\/p>\r\n\r\n<ul>\r\n\t<li>1 &le;&nbsp;T&nbsp;&le; 100.<\/li>\r\n\t<li>0 &le;&nbsp;N&nbsp;&le; 10<sup>6<\/sup>.<\/li>\r\n<\/ul>\r\n","output":"<p>\uac01 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574\uc11c, \ucf00\uc774\uc2a4 \ubc88\ud638\uac00 x\uc774\uace0 y\uac00 \uc815\ub2f5\uc77c \ub54c, Case #x: y\ub77c\uace0 \ucd9c\ub825\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n","hint":"<p dir=\"ltr\">\uc608\uc81c \uc785\ucd9c\ub825 1\ubc88\uc5d0 \ub300\ud574\uc11c, 2 &times; 0 = 0, 3 &times; 0 = 0 \ub4f1\ub4f1\uc73c\ub85c \uc774\uc5b4\uc9c0\ubbc0\ub85c, \ube14\ub9ac\ud2b8\ub9ad\uc2a4\ub294 0\uc678\uc5d0\ub294 \ub2e4\ub978 \uc22b\uc790\ub97c \uae30\ub85d\ud560 \uc218 \uc5c6\uc744 \uac83\uc774\uba70, \ub530\ub77c\uc11c \uc601\uc6d0\ud788 \uc7a0\uc5d0 \ub4e4 \uc218 \uc5c6\ub2e4.<\/p>\r\n\r\n<p dir=\"ltr\">\uc608\uc81c \uc785\ucd9c\ub825 2\ubc88\uc758 \uacbd\uc6b0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \uc21c\uc73c\ub85c \ub5a0\uc62c\ub9b4 \uac83\uc774\uba70, 0\uc774 \uac00\uc7a5 \ub9c8\uc9c0\ub9c9\uc5d0 \uae30\ub85d\ub418\ub294 \uc218\uac00 \ub420 \uac83\uc774\ub2e4. \ub530\ub77c\uc11c 10\uc774 \ub9c8\uc9c0\ub9c9 \uc218\uac00 \ub420 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p dir=\"ltr\">\uc608\uc81c \uc785\ucd9c\ub825 3\ubc88\uc758 \uacbd\uc6b0, 2, 4, 6... \ub4f1\ub4f1\uc73c\ub85c \ub5a0\uc62c\ub9b4 \uac83\uc774\ub2e4. \uc22b\uc790 9\ub294 90 \uc804\uc5d0\ub294 \uae30\ub85d\ud560 \uc218 \uc5c6\ub2e4. 90\uc744 \ub5a0\uc62c\ub838\uc744 \ub54c \uc774\ubbf8 \ube14\ub9ac\ud2b8\ub9ad\uc2a4\ub294 0~8\uc758 \uc22b\uc790\ub97c \uc801\uc5c8\uc744 \uac83\uc774\ubbc0\ub85c, 90\uc774 \ub9c8\uc9c0\ub9c9 \uc218\uac00 \ub420 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p dir=\"ltr\">\uc608\uc81c \uc785\ucd9c\ub825 4\ubc88\uc740 \ube14\ub9ac\ud2b8\ub9ad\uc2a4\uac00 11, 22, 33, 44, 55, 66, 77, 88, 99, 110 \uc744 \ub5a0\uc62c\ub9b4 \uac83\uc774\uace0, 110\uc774 \ub9c8\uc9c0\ub9c9 \uc218\uac00 \ub420 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc608\uc81c \uc785\ucd9c\ub825 5\ubc88\uc740 \ubb38\uc81c\uc5d0\uc11c \uc124\uba85\ud55c \uc218\uc774\ub2e4.<\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"14382","problem_lang":"1","title":"Counting Sheep (Large)","description":"<p>Bleatrix Trotter the sheep has devised a strategy that helps her fall asleep faster. First, she picks a number&nbsp;N. Then she starts naming&nbsp;N, 2 &times;&nbsp;N, 3 &times;&nbsp;N, and so on. Whenever she names a number, she thinks about all of the digits in that number. She keeps track of which digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) she has seen at least once so far as part of any number she has named. Once she has seen each of the ten digits at least once, she will fall asleep.<\/p>\r\n\r\n<p>Bleatrix must start with&nbsp;N&nbsp;and must always name (i&nbsp;+ 1) &times;&nbsp;N&nbsp;directly after&nbsp;i&nbsp;&times;&nbsp;N. For example, suppose that Bleatrix picks&nbsp;N&nbsp;= 1692. She would count as follows:<\/p>\r\n\r\n<ul>\r\n\t<li>N&nbsp;= 1692. Now she has seen the digits 1, 2, 6, and 9.<\/li>\r\n\t<li>2N&nbsp;= 3384. Now she has seen the digits 1, 2, 3, 4, 6, 8, and 9.<\/li>\r\n\t<li>3N&nbsp;= 5076. Now she has seen all ten digits, and falls asleep.<\/li>\r\n<\/ul>\r\n\r\n<p>What is the last number that she will name before falling asleep? If she will count forever, print&nbsp;<code>INSOMNIA<\/code>&nbsp;instead.<\/p>\r\n","input":"<p>The first line of the input gives the number of test cases,&nbsp;T.&nbsp;T&nbsp;test cases follow. Each consists of one line with a single integer&nbsp;N, the number Bleatrix has chosen.<\/p>\r\n\r\n<h3>Limits<\/h3>\r\n\r\n<ul>\r\n\t<li>1 &le;&nbsp;T&nbsp;&le; 100.<\/li>\r\n\t<li>0 &le;&nbsp;N&nbsp;&le; 10<sup>6<\/sup>.<\/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 the last number that Bleatrix will name before falling asleep, according to the rules described in the statement.<\/p>\r\n","hint":"<p>In Case #1, since 2 &times; 0 = 0, 3 &times; 0 = 0, and so on, Bleatrix will never see any digit other than 0, and so she will count forever and never fall asleep. Poor sheep!<\/p>\r\n\r\n<p>In Case #2, Bleatrix will name 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. The 0 will be the last digit needed, and so she will fall asleep after 10.<\/p>\r\n\r\n<p>In Case #3, Bleatrix will name 2, 4, 6... and so on. She will not see the digit 9 in any number until 90, at which point she will fall asleep. By that point, she will have already seen the digits 0, 1, 2, 3, 4, 5, 6, 7, and 8, which will have appeared for the first time in the numbers 10, 10, 2, 30, 4, 50, 6, 70, and 8, respectively.<\/p>\r\n\r\n<p>In Case #4, Bleatrix will name 11, 22, 33, 44, 55, 66, 77, 88, 99, 110 and then fall asleep.<\/p>\r\n\r\n<p>Case #5 is the one described in the problem statement. Note that it would only show up in the Large dataset, and not in the Small dataset.<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"English"}]

채점 및 기타 정보

  • 예제는 채점하지 않는다.