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문제

당신이 한 버스 정거장에 아침 9시에 도착했다. 그리고 9시부터 9시 59분까지 그 곳에 있었다. 그 동안 노선이 다른 여러 버스들이 이 정거장에 섰는데, 당신은 그 버스들이 도착하는 시각을 주의 깊게 관찰하였다.

노선이 같은 버스는 9시 정각부터 9분까지 같은 시간 간격으로 규칙성 있게 도착한다. 버스를 관찰한 시간은 0부터 59분까지이다. 각 노선을 달리는 버스는 그 동안 적어도 두 번은 정거장에 서며, 시간은 정수 시간만을 계산한다. (최소 단위는 1분)

노선이 다르더라도 어떤 버스 노선의 시간 스케줄은 최초 도착 시간이나 시간 간격 중 하나 이상이 다른 노선의 스케줄과 일치할 수 있다. 그런 이유로, 같은 시각에 노선이 다른 버스가 두 대 이상 도착하면 그 시각은 온 버스 수만큼 중복 기록한다. 즉, 만약 최초 도착 시간과 오는 간격이 완전히 같은 두 노선이 있더라도 그 노선을 다니는 버스들이 온 시각은 구분되어 따로 입력 파일에 기록된다는 뜻이다.

버스가 도착한 시간 기록을 입력 받아서 이 간격대로 있을 수 있는 서로 다른 버스 노선들을 구해 이들의 시간 스케줄을 출력하는 프로그램을 작성하라. 그리고 찾아낸 버스 노선마다 그 노선의 첫 도착 시간과 다음 간격을 출력하라. 그러한 경우가 많다면, 버스 노선의 수가 가장 적은 경우를 찾아야 한다. (버스의 수는 25를 넘지 않는다)

입력

첫째 줄에 버스가 선 횟수 n(2≤n≤300)이 주어진다. 다음 줄에는 버스가 온 시각 n개가 주어진다. 각각의 시각은 정수라 가정하자. 시각은 분 단위만 기록하며, 0이상 59이하의 값을 갖는다. 입력의 중간에는 공백 대신 엔터가 주어질 수도 있다.

출력

첫째 줄에 버스 노선의 최소 개수 X를 출력한다. 다음 X개의 줄에는 각 노선의 첫 도착 시각과 간격을 출력한다. 최적해가 여러 개인 경우에는 임의의 하나만 출력하면 되며, 출력 순서는 상관이 없다.

예제 입력 1

17
0 3 5 13 13 15
21 26 27 29
37 39 39 45 51 52 53

예제 출력 1

3
0 13
3 12
5 8

힌트

0 13    ← 0 . . 13  .  . 26  .  .  . 39  .  . 52  . (5번)
3 12    ← . 3 .  . 15  .  . 27  .  . 39  . 51  .  . (5번)
5 8     ← . . 5 13  . 21  .  . 29 37  . 45  .  . 53 (7번)
[{"problem_id":"1973","problem_lang":"0","title":"\ubc84\uc2a4 \ub178\uc120","description":"<p>\ub2f9\uc2e0\uc774 \ud55c \ubc84\uc2a4 \uc815\uac70\uc7a5\uc5d0 \uc544\uce68 9\uc2dc\uc5d0 \ub3c4\ucc29\ud588\ub2e4. \uadf8\ub9ac\uace0 9\uc2dc\ubd80\ud130 9\uc2dc 59\ubd84\uae4c\uc9c0 \uadf8 \uacf3\uc5d0 \uc788\uc5c8\ub2e4. \uadf8 \ub3d9\uc548 \ub178\uc120\uc774 \ub2e4\ub978 \uc5ec\ub7ec \ubc84\uc2a4\ub4e4\uc774 \uc774 \uc815\uac70\uc7a5\uc5d0 \uc130\ub294\ub370, \ub2f9\uc2e0\uc740 \uadf8 \ubc84\uc2a4\ub4e4\uc774 \ub3c4\ucc29\ud558\ub294 \uc2dc\uac01\uc744 \uc8fc\uc758 \uae4a\uac8c \uad00\ucc30\ud558\uc600\ub2e4.<\/p>\r\n\r\n<p>\ub178\uc120\uc774 \uac19\uc740 \ubc84\uc2a4\ub294 9\uc2dc \uc815\uac01\ubd80\ud130 9\ubd84\uae4c\uc9c0 \uac19\uc740 \uc2dc\uac04 \uac04\uaca9\uc73c\ub85c \uaddc\uce59\uc131 \uc788\uac8c \ub3c4\ucc29\ud55c\ub2e4. \ubc84\uc2a4\ub97c \uad00\ucc30\ud55c \uc2dc\uac04\uc740 0\ubd80\ud130 59\ubd84\uae4c\uc9c0\uc774\ub2e4. \uac01 \ub178\uc120\uc744 \ub2ec\ub9ac\ub294 \ubc84\uc2a4\ub294 \uadf8 \ub3d9\uc548 \uc801\uc5b4\ub3c4 \ub450 \ubc88\uc740 \uc815\uac70\uc7a5\uc5d0 \uc11c\uba70, \uc2dc\uac04\uc740 \uc815\uc218 \uc2dc\uac04\ub9cc\uc744 \uacc4\uc0b0\ud55c\ub2e4. (\ucd5c\uc18c \ub2e8\uc704\ub294 1\ubd84)<\/p>\r\n\r\n<p>\ub178\uc120\uc774 \ub2e4\ub974\ub354\ub77c\ub3c4 \uc5b4\ub5a4 \ubc84\uc2a4 \ub178\uc120\uc758 \uc2dc\uac04 \uc2a4\ucf00\uc904\uc740 \ucd5c\ucd08 \ub3c4\ucc29 \uc2dc\uac04\uc774\ub098 \uc2dc\uac04 \uac04\uaca9 \uc911 \ud558\ub098 \uc774\uc0c1\uc774 \ub2e4\ub978 \ub178\uc120\uc758 \uc2a4\ucf00\uc904\uacfc \uc77c\uce58\ud560 \uc218 \uc788\ub2e4. \uadf8\ub7f0 \uc774\uc720\ub85c, \uac19\uc740 \uc2dc\uac01\uc5d0 \ub178\uc120\uc774 \ub2e4\ub978 \ubc84\uc2a4\uac00 \ub450 \ub300 \uc774\uc0c1 \ub3c4\ucc29\ud558\uba74 \uadf8 \uc2dc\uac01\uc740 \uc628 \ubc84\uc2a4 \uc218\ub9cc\ud07c \uc911\ubcf5 \uae30\ub85d\ud55c\ub2e4. \uc989, \ub9cc\uc57d \ucd5c\ucd08 \ub3c4\ucc29 \uc2dc\uac04\uacfc \uc624\ub294 \uac04\uaca9\uc774 \uc644\uc804\ud788 \uac19\uc740 \ub450 \ub178\uc120\uc774 \uc788\ub354\ub77c\ub3c4 \uadf8 \ub178\uc120\uc744 \ub2e4\ub2c8\ub294 \ubc84\uc2a4\ub4e4\uc774 \uc628 \uc2dc\uac01\uc740 \uad6c\ubd84\ub418\uc5b4 \ub530\ub85c \uc785\ub825 \ud30c\uc77c\uc5d0 \uae30\ub85d\ub41c\ub2e4\ub294 \ub73b\uc774\ub2e4.<\/p>\r\n\r\n<p>\ubc84\uc2a4\uac00 \ub3c4\ucc29\ud55c \uc2dc\uac04 \uae30\ub85d\uc744 \uc785\ub825 \ubc1b\uc544\uc11c \uc774 \uac04\uaca9\ub300\ub85c \uc788\uc744 \uc218 \uc788\ub294 \uc11c\ub85c \ub2e4\ub978 \ubc84\uc2a4 \ub178\uc120\ub4e4\uc744 \uad6c\ud574 \uc774\ub4e4\uc758 \uc2dc\uac04 \uc2a4\ucf00\uc904\uc744 \ucd9c\ub825\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\ub77c. \uadf8\ub9ac\uace0 \ucc3e\uc544\ub0b8 \ubc84\uc2a4 \ub178\uc120\ub9c8\ub2e4 \uadf8 \ub178\uc120\uc758 \uccab \ub3c4\ucc29 \uc2dc\uac04\uacfc \ub2e4\uc74c \uac04\uaca9\uc744 \ucd9c\ub825\ud558\ub77c. \uadf8\ub7ec\ud55c \uacbd\uc6b0\uac00 \ub9ce\ub2e4\uba74, \ubc84\uc2a4 \ub178\uc120\uc758 \uc218\uac00 \uac00\uc7a5 \uc801\uc740 \uacbd\uc6b0\ub97c \ucc3e\uc544\uc57c \ud55c\ub2e4. (\ubc84\uc2a4\uc758 \uc218\ub294 25\ub97c \ub118\uc9c0 \uc54a\ub294\ub2e4)<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ubc84\uc2a4\uac00 \uc120 \ud69f\uc218 n(2&le;n&le;300)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ub2e4\uc74c \uc904\uc5d0\ub294 \ubc84\uc2a4\uac00 \uc628 \uc2dc\uac01 n\uac1c\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01\uac01\uc758 \uc2dc\uac01\uc740 \uc815\uc218\ub77c \uac00\uc815\ud558\uc790. \uc2dc\uac01\uc740 \ubd84 \ub2e8\uc704\ub9cc \uae30\ub85d\ud558\uba70, 0\uc774\uc0c1 59\uc774\ud558\uc758 \uac12\uc744 \uac16\ub294\ub2e4. \uc785\ub825\uc758 \uc911\uac04\uc5d0\ub294 \uacf5\ubc31 \ub300\uc2e0 \uc5d4\ud130\uac00 \uc8fc\uc5b4\uc9c8 \uc218\ub3c4 \uc788\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \ubc84\uc2a4 \ub178\uc120\uc758 \ucd5c\uc18c \uac1c\uc218 X\ub97c \ucd9c\ub825\ud55c\ub2e4. \ub2e4\uc74c X\uac1c\uc758 \uc904\uc5d0\ub294 \uac01 \ub178\uc120\uc758 \uccab \ub3c4\ucc29 \uc2dc\uac01\uacfc \uac04\uaca9\uc744 \ucd9c\ub825\ud55c\ub2e4. \ucd5c\uc801\ud574\uac00 \uc5ec\ub7ec \uac1c\uc778 \uacbd\uc6b0\uc5d0\ub294 \uc784\uc758\uc758 \ud558\ub098\ub9cc \ucd9c\ub825\ud558\uba74 \ub418\uba70, \ucd9c\ub825 \uc21c\uc11c\ub294 \uc0c1\uad00\uc774 \uc5c6\ub2e4.<\/p>\r\n","hint":"<pre>\r\n0 13    &larr; 0 . . 13  .  . 26  .  .  . 39  .  . 52  . (5\ubc88)\r\n3 12    &larr; . 3 .  . 15  .  . 27  .  . 39  . 51  .  . (5\ubc88)\r\n5 8     &larr; . . 5 13  . 21  .  . 29 37  . 45  .  . 53 (7\ubc88)<\/pre>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"1973","problem_lang":"1","title":"The Buses","description":"<p>A man arrives at a bus stop at 12:00. He remains there during 12:00-12:59. The bus stop is used by a number of bus routes. The man notes the times of arriving buses. The times when buses arrive are given.<\/p>\r\n\r\n<ul>\r\n\t<li>Buses on the same route arrive at regular intervals from 12:00 to 12:59 throughout the entire hour.<\/li>\r\n\t<li>Times are given in whole minutes from 0 to 59.<\/li>\r\n\t<li>Each bus route stops at least 2 times.<\/li>\r\n\t<li>The number of bus routes in the test examples will be &lt;=17.<\/li>\r\n\t<li>Buses from different routes may arrive at the same time.<\/li>\r\n\t<li>Several bus routes can have the same time of first arrival and\/or time interval. If two bus routes have the same starting time and interval, they are distinct and are both to be presented.<\/li>\r\n<\/ul>\r\n\r\n<p>Find the schedule with the fewest number of bus routes that must stop at the bus stop to satisfy the input data. For each bus route, output the starting time and the interval.<\/p>\r\n","input":"<p>The input contains a number n (n&lt;=300) telling how many arriving buses have been noted, followed by the arrival times in ascending order.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","output":"<p>Write a table to the output with one line for each bus route. Each line in the file gives the time of arrival for the first bus and the time interval in minutes. The order of the bus routes does not matter. If there are several solutions, only one is required.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

Olympiad > International Olympiad in Informatics > IOI 1994 5번