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문제

선영이는 대형 병원에서 사용하는 인사 관리 프로그램을 만들고 있다. 가장 먼저 만들고 있는 부분은 직원들의 휴가 관리 프로그램이다.

병원에서 일하는 간호사는 두 종류가 있다. 일반 간호사는 입원해 있는 환자를 간호하는 간호사이고, 특수 간호사는 "수술 간호사", "간호부장"과 같이 특별히 맡은 자리가 있는 간호사이다.

일반 간호사가 휴가를 갔을 때는 다른 간호사가 그 간호사의 업무를 대신해 주면 되기 때문에, 큰 문제가 생기지 않는다. 하지만, 특수 간호사는 반드시 대체자가 있어야지만 휴가를 갈 수 있다. 따라서, 모든 특수 간호사는 자신을 대체할 수 있는 간호사의 목록을 가지고 있다. 만약, 대체 간호사도 특수 간호사인 경우에는 그 대체 간호사도 대체할 간호사를 찾아야 한다. 가끔, 특수 간호사는 대체를 할 수 없어서 휴가를 갈 수 없는 경우도 있다.

아래와 같은 예를 보자. 이 병원에는 총 일곱 명의 간호사가 있다. Alice, Bob, Clara, Dona, Emma는 특수 간호사이고, Fiona, Gloria는 일반 간호사이다. 누가 누구를 대체할 수 있는지는 아래 그림에 화살표로 나타나있다. (A에서 B로 가는 화살표는 A가 B를 대체할 수 있다는 의미)

위의 예제에서 Dona와 Emma는 휴가를 절대로 갈 수 없다. 그 이유는 서로가 서로를 대체하기 때문에, 한 명이 휴가를 갔을 때, 휴가를 가지 않은 한 사람이 두 업무를 동시에 맡을 수 없기 때문이다. Alice, Bob, Clara는 휴가에 갈 수 있다. 하지만, Gloria는 동시에 Bob과 Clara를 대체할 수 없기 때문에, Bob과 Clara는 동시에 휴가를 갈 수 없다.

간호사의 정보가 주어졌을 때, 휴가를 절대로 갈 수 없는 간호사와 휴가를 갈 수는 있지만, 동시에 휴가를 갈 수 없는 간호사의 쌍을 구하는 프로그램을 작성하시오.

입력

첫째 줄에 간호사의 수 n과 특수 간호사의 수 k가 주어진다. 간호사 1번부터 k번까지는 특수 간호사, k+1번부터 n번까지는 일반 간호사이다. (1 ≤ k < n ≤ 1000)

다음 k개 줄에는 가능한 대체 정보가 주어진다. (i+1)번째 줄의 첫 번째 숫자는 i번 간호사를 대체할 수 있는 간호사의 수 di이다. 다음 di개의 숫자는 그 간호사를 대체할 수 있는 간호사의 번호이다. 전체 리스트의 길이는 10,000을 넘지 않는다.

출력

첫째 줄에 절대로 휴가를 갈 수 없는 간호사의 수를 출력하고, 다음 줄에는 그러한 간호사의 번호를 모두 출력한다.

다음 줄에는 휴가를 갈 수는 있지만, 동시에 휴가를 갈 수 없는 간호사 쌍의 수를 출력한다. 만약, 쌍의 수가 10,000보다 작거나 같다면, 다음 줄부터 한 줄에 하나씩 그러한 쌍을 출력한다. (쌍 (A,B)와 (B,A)는 같은 쌍이다)

예제 입력 1

7 5
2 6 7
1 7
2 2 7
1 5
1 4

예제 출력 1

2
4 5
3
2 3
2 7
3 7
[{"problem_id":"7777","problem_lang":"0","title":"\ubcd1\uc6d0","description":"<p>\uc120\uc601\uc774\ub294 \ub300\ud615 \ubcd1\uc6d0\uc5d0\uc11c \uc0ac\uc6a9\ud558\ub294 \uc778\uc0ac \uad00\ub9ac \ud504\ub85c\uadf8\ub7a8\uc744 \ub9cc\ub4e4\uace0 \uc788\ub2e4. \uac00\uc7a5 \uba3c\uc800 \ub9cc\ub4e4\uace0 \uc788\ub294 \ubd80\ubd84\uc740 \uc9c1\uc6d0\ub4e4\uc758 \ud734\uac00 \uad00\ub9ac \ud504\ub85c\uadf8\ub7a8\uc774\ub2e4.<\/p>\r\n\r\n<p>\ubcd1\uc6d0\uc5d0\uc11c \uc77c\ud558\ub294 \uac04\ud638\uc0ac\ub294 \ub450 \uc885\ub958\uac00 \uc788\ub2e4. \uc77c\ubc18 \uac04\ud638\uc0ac\ub294 \uc785\uc6d0\ud574 \uc788\ub294 \ud658\uc790\ub97c \uac04\ud638\ud558\ub294 \uac04\ud638\uc0ac\uc774\uace0, \ud2b9\uc218 \uac04\ud638\uc0ac\ub294 &quot;\uc218\uc220 \uac04\ud638\uc0ac&quot;, &quot;\uac04\ud638\ubd80\uc7a5&quot;\uacfc \uac19\uc774 \ud2b9\ubcc4\ud788 \ub9e1\uc740 \uc790\ub9ac\uac00 \uc788\ub294 \uac04\ud638\uc0ac\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc77c\ubc18 \uac04\ud638\uc0ac\uac00 \ud734\uac00\ub97c \uac14\uc744 \ub54c\ub294 \ub2e4\ub978 \uac04\ud638\uc0ac\uac00 \uadf8 \uac04\ud638\uc0ac\uc758 \uc5c5\ubb34\ub97c \ub300\uc2e0\ud574 \uc8fc\uba74 \ub418\uae30 \ub54c\ubb38\uc5d0, \ud070 \ubb38\uc81c\uac00 \uc0dd\uae30\uc9c0 \uc54a\ub294\ub2e4. \ud558\uc9c0\ub9cc, \ud2b9\uc218 \uac04\ud638\uc0ac\ub294 \ubc18\ub4dc\uc2dc \ub300\uccb4\uc790\uac00 \uc788\uc5b4\uc57c\uc9c0\ub9cc \ud734\uac00\ub97c \uac08 \uc218 \uc788\ub2e4. \ub530\ub77c\uc11c, \ubaa8\ub4e0 \ud2b9\uc218 \uac04\ud638\uc0ac\ub294 \uc790\uc2e0\uc744 \ub300\uccb4\ud560 \uc218 \uc788\ub294 \uac04\ud638\uc0ac\uc758 \ubaa9\ub85d\uc744 \uac00\uc9c0\uace0 \uc788\ub2e4. \ub9cc\uc57d, \ub300\uccb4 \uac04\ud638\uc0ac\ub3c4 \ud2b9\uc218 \uac04\ud638\uc0ac\uc778 \uacbd\uc6b0\uc5d0\ub294 \uadf8 \ub300\uccb4 \uac04\ud638\uc0ac\ub3c4 \ub300\uccb4\ud560 \uac04\ud638\uc0ac\ub97c \ucc3e\uc544\uc57c \ud55c\ub2e4. \uac00\ub054, \ud2b9\uc218 \uac04\ud638\uc0ac\ub294 \ub300\uccb4\ub97c \ud560 \uc218 \uc5c6\uc5b4\uc11c \ud734\uac00\ub97c \uac08 \uc218 \uc5c6\ub294 \uacbd\uc6b0\ub3c4 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc544\ub798\uc640 \uac19\uc740 \uc608\ub97c \ubcf4\uc790. \uc774 \ubcd1\uc6d0\uc5d0\ub294 \ucd1d \uc77c\uacf1 \uba85\uc758 \uac04\ud638\uc0ac\uac00 \uc788\ub2e4. Alice, Bob, Clara, Dona, Emma\ub294 \ud2b9\uc218 \uac04\ud638\uc0ac\uc774\uace0, Fiona, Gloria\ub294 \uc77c\ubc18 \uac04\ud638\uc0ac\uc774\ub2e4. \ub204\uac00 \ub204\uad6c\ub97c \ub300\uccb4\ud560 \uc218 \uc788\ub294\uc9c0\ub294 \uc544\ub798 \uadf8\ub9bc\uc5d0 \ud654\uc0b4\ud45c\ub85c \ub098\ud0c0\ub098\uc788\ub2e4. (A\uc5d0\uc11c B\ub85c \uac00\ub294 \ud654\uc0b4\ud45c\ub294 A\uac00 B\ub97c \ub300\uccb4\ud560 \uc218 \uc788\ub2e4\ub294 \uc758\ubbf8)<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/nurse.png\" style=\"height:92px; width:434px\" \/><\/p>\r\n\r\n<p>\uc704\uc758 \uc608\uc81c\uc5d0\uc11c Dona\uc640 Emma\ub294 \ud734\uac00\ub97c \uc808\ub300\ub85c \uac08 \uc218 \uc5c6\ub2e4. \uadf8 \uc774\uc720\ub294 \uc11c\ub85c\uac00 \uc11c\ub85c\ub97c \ub300\uccb4\ud558\uae30 \ub54c\ubb38\uc5d0, \ud55c \uba85\uc774 \ud734\uac00\ub97c \uac14\uc744 \ub54c, \ud734\uac00\ub97c \uac00\uc9c0 \uc54a\uc740 \ud55c \uc0ac\ub78c\uc774 \ub450 \uc5c5\ubb34\ub97c \ub3d9\uc2dc\uc5d0 \ub9e1\uc744 \uc218 \uc5c6\uae30 \ub54c\ubb38\uc774\ub2e4. Alice, Bob, Clara\ub294 \ud734\uac00\uc5d0 \uac08 \uc218 \uc788\ub2e4. \ud558\uc9c0\ub9cc, Gloria\ub294 \ub3d9\uc2dc\uc5d0 Bob\uacfc Clara\ub97c \ub300\uccb4\ud560 \uc218 \uc5c6\uae30 \ub54c\ubb38\uc5d0, Bob\uacfc Clara\ub294 \ub3d9\uc2dc\uc5d0 \ud734\uac00\ub97c \uac08 \uc218 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\uac04\ud638\uc0ac\uc758 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ud734\uac00\ub97c \uc808\ub300\ub85c \uac08 \uc218 \uc5c6\ub294 \uac04\ud638\uc0ac\uc640 \ud734\uac00\ub97c \uac08 \uc218\ub294 \uc788\uc9c0\ub9cc, \ub3d9\uc2dc\uc5d0 \ud734\uac00\ub97c \uac08 \uc218 \uc5c6\ub294 \uac04\ud638\uc0ac\uc758 \uc30d\uc744 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \uac04\ud638\uc0ac\uc758 \uc218 n\uacfc \ud2b9\uc218 \uac04\ud638\uc0ac\uc758 \uc218 k\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac04\ud638\uc0ac 1\ubc88\ubd80\ud130 k\ubc88\uae4c\uc9c0\ub294 \ud2b9\uc218 \uac04\ud638\uc0ac, k+1\ubc88\ubd80\ud130 n\ubc88\uae4c\uc9c0\ub294 \uc77c\ubc18 \uac04\ud638\uc0ac\uc774\ub2e4. (1 &le; k &lt; n &le; 1000)<\/p>\r\n\r\n<p>\ub2e4\uc74c k\uac1c \uc904\uc5d0\ub294 \uac00\ub2a5\ud55c \ub300\uccb4 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (i+1)\ubc88\uc9f8 \uc904\uc758 \uccab \ubc88\uc9f8 \uc22b\uc790\ub294 i\ubc88 \uac04\ud638\uc0ac\ub97c \ub300\uccb4\ud560 \uc218 \uc788\ub294 \uac04\ud638\uc0ac\uc758 \uc218 d<sub>i<\/sub>\uc774\ub2e4. \ub2e4\uc74c d<sub>i<\/sub>\uac1c\uc758 \uc22b\uc790\ub294 \uadf8 \uac04\ud638\uc0ac\ub97c \ub300\uccb4\ud560 \uc218 \uc788\ub294 \uac04\ud638\uc0ac\uc758 \ubc88\ud638\uc774\ub2e4. \uc804\uccb4 \ub9ac\uc2a4\ud2b8\uc758 \uae38\uc774\ub294 10,000\uc744 \ub118\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc808\ub300\ub85c \ud734\uac00\ub97c \uac08 \uc218 \uc5c6\ub294 \uac04\ud638\uc0ac\uc758 \uc218\ub97c \ucd9c\ub825\ud558\uace0, \ub2e4\uc74c \uc904\uc5d0\ub294 \uadf8\ub7ec\ud55c \uac04\ud638\uc0ac\uc758 \ubc88\ud638\ub97c \ubaa8\ub450 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\uc74c \uc904\uc5d0\ub294 \ud734\uac00\ub97c \uac08 \uc218\ub294 \uc788\uc9c0\ub9cc, \ub3d9\uc2dc\uc5d0 \ud734\uac00\ub97c \uac08 \uc218 \uc5c6\ub294 \uac04\ud638\uc0ac \uc30d\uc758 \uc218\ub97c \ucd9c\ub825\ud55c\ub2e4. \ub9cc\uc57d, \uc30d\uc758 \uc218\uac00 10,000\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\ub2e4\uba74, \ub2e4\uc74c \uc904\ubd80\ud130 \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \uadf8\ub7ec\ud55c \uc30d\uc744 \ucd9c\ub825\ud55c\ub2e4. (\uc30d (A,B)\uc640 (B,A)\ub294 \uac19\uc740 \uc30d\uc774\ub2e4)<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"7777","problem_lang":"1","title":"Hospital","description":"<p>You are writing a personnel management tool for a large hospital. One of the problems is managing the vacation plans of employees.<\/p>\r\n\r\n<p>There are two types of nurses working in the hospital: sta\ufb00 nurses continuously take care of the patients and special nurses \ufb01ll special positions like &ldquo;surgical nurse&rdquo; or &ldquo;nurse supervisor&rdquo;. When a sta\ufb00 nurse goes on vacation, nothing critical happens, because other nurses will do her work. But when special nurse goes on vacation, she must be substituted. For every special nurse there is a list of nurses, who can substitute her. If the substituting nurse is a special nurse too, then some third nurse must substitute her as well, and so on. Sometimes it is impossible for special nurse to go on vacation, because there is no sequence of substitutions, after that all special nurse positions are \ufb01lled.<\/p>\r\n\r\n<p>Consider the following example. There are seven nurses in a hospital. Alice, Bob, Clara, Dona and Emma are special nurses, Fiona and Gloria are sta\ufb00 nurses. They can substitute each other according to the following scheme (arrow from A to B means A can substitute B):<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/nurse.png\" style=\"height:92px; width:434px\" \/><\/p>\r\n\r\n<p>In this example, Dona and Emma cannot go on vacation, because if one of them does, another cannot \ufb01ll both positions. Alice, Bob and Clara can go on vacation, but Bob and Clara cannot do it at the same time, because Gloria cannot substitute them both simultaneously.<\/p>\r\n\r\n<p>Your task is to \ufb01nd all nurses who cannot go on vacation, and all pairs of nurses, such that both can go on vacation, but not in the same time.<\/p>\r\n","input":"<p>The \ufb01rst line of the input \ufb01le contains two integer numbers n and k &mdash; the total number of nurses and number of special nurses. Nurses 1 ... k are special nurses, and nurses k + 1 ... n are sta\ufb00 nurses (1 &le; k &lt; n &le; 1000). Next k lines contain the lists of possible substitutions. The \ufb01rst number in (i+1)-th line is d<sub>i<\/sub> &mdash; the number of nurses, who can substitute i-th nurse. Following d<sub>i<\/sub> numbers in the same line are the indices of substituting nurses. The total length of all lists does not exceed 10 000.<\/p>\r\n","output":"<p>First output the number of nurses who cannot go on vacation. Then output their indices.<\/p>\r\n\r\n<p>After that, output the number of pairs of nurses, such that both can go on vacation, but not at the same time. Finally, if the number of such pairs is not greater then 10 000, output all these pairs (pairs (A,&nbsp;B) and (B,&nbsp;A) are considered equal).<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]