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문제

학생들은 스타 대회를 열기로 했다. 참가자는 총 N명으로 1번부터 N번까지 번호가 붙어있다. 토너먼트의 규칙은 다음과 같다. 게임이 진행되는 동안 남아있는 참가자 중 임의의 두 명을 뽑아 스타를 붙인다. 경기 후 패자는 탈락되고 승자는 계속해서 대회에 참가하게 된다. (단, 무승부는 존재하지 않는다.) 결국 N-1번의 게임을 하면 최후의 승자가 남게 되고 이 학생이 우승을 하게 된다.


참가자 중 어떤 한 학생이 다른 한 학생을 항상 이기는 천적 관계가 존재한다. 즉, 이 두 학생끼리는 경기를 펼치지 않아도 누가 이긴다는 것을 알 수 있다는 것이다. 예를 들어, 위와 같은 그래프에서 1번은 2, 3번을 항상 이긴다는 뜻이다. 하지만 1번과 4번이 경기하면 1번이 이길 수도 있고 4번이 이길 수도 있다.

N명의 참가자에 대한 천적 관계가 주어졌을 때 우승 가능성이 있는 학생들을 알 수 있다. 예를 들어, 위의 예에서 3번 학생은 1번 학생한테 항상 지지만 4번 학생과 1번 학생이 경기를 하여 1번 학생이 탈락한 후 3번 학생이 2, 4번 학생을 차례대로 이기고 우승할 수 있기 때문에 우승 가능성이 있는 학생이다.

문제는 N명의 참가자에 대한 천적 관계가 주어지면 우승 가능성이 있는 학생들을 모두 구하는 것이다.

입력

첫째 줄에 참가자 수 N(1≤N≤100,000)이 주어진다. 다음 N개의 줄에 천적관계가 주어지는데 i+1번째 줄에는 i번째 학생이 항상 이기는 학생의 수 와 이 학생들의 번호가 공백으로 구분되어 증가하는 순서로 주어진다. (단, 자기 자신이 천적인 경우는 없다.) 천적 관계의 총 수는 1,000,000을 넘지 않는다.

출력

첫째 줄에 우승 가능성이 있는 학생 수 w와 이 학생들의 번호를 오름차순으로 공백으로 구분하여 출력한다.

예제 입력 1

4
2 2 3
0
1 2
1 2

예제 출력 1

3 1 3 4

힌트

[{"problem_id":"1608","problem_lang":"0","title":"\uc2a4\ud0c0 \ub300\ud68c","description":"<p>\ud559\uc0dd\ub4e4\uc740 \uc2a4\ud0c0 \ub300\ud68c\ub97c \uc5f4\uae30\ub85c \ud588\ub2e4. \ucc38\uac00\uc790\ub294 \ucd1d N\uba85\uc73c\ub85c 1\ubc88\ubd80\ud130 N\ubc88\uae4c\uc9c0 \ubc88\ud638\uac00 \ubd99\uc5b4\uc788\ub2e4. \ud1a0\ub108\uba3c\ud2b8\uc758 \uaddc\uce59\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4. \uac8c\uc784\uc774 \uc9c4\ud589\ub418\ub294 \ub3d9\uc548 \ub0a8\uc544\uc788\ub294 \ucc38\uac00\uc790 \uc911 \uc784\uc758\uc758 \ub450 \uba85\uc744 \ubf51\uc544 \uc2a4\ud0c0\ub97c \ubd99\uc778\ub2e4. \uacbd\uae30 \ud6c4 \ud328\uc790\ub294 \ud0c8\ub77d\ub418\uace0 \uc2b9\uc790\ub294 \uacc4\uc18d\ud574\uc11c \ub300\ud68c\uc5d0 \ucc38\uac00\ud558\uac8c \ub41c\ub2e4. (\ub2e8, \ubb34\uc2b9\ubd80\ub294 \uc874\uc7ac\ud558\uc9c0 \uc54a\ub294\ub2e4.) \uacb0\uad6d N-1\ubc88\uc758 \uac8c\uc784\uc744 \ud558\uba74 \ucd5c\ud6c4\uc758 \uc2b9\uc790\uac00 \ub0a8\uac8c \ub418\uace0 \uc774 \ud559\uc0dd\uc774 \uc6b0\uc2b9\uc744 \ud558\uac8c \ub41c\ub2e4.<\/p>\r\n<p><br \/>\r\n<img width=\"133\" height=\"171\" alt=\"\" src=\"\/upload\/201004\/star.png\" \/><\/p>\r\n<p>\ucc38\uac00\uc790 \uc911 \uc5b4\ub5a4 \ud55c \ud559\uc0dd\uc774 \ub2e4\ub978 \ud55c \ud559\uc0dd\uc744 \ud56d\uc0c1 \uc774\uae30\ub294 \ucc9c\uc801 \uad00\uacc4\uac00 \uc874\uc7ac\ud55c\ub2e4. \uc989, \uc774 \ub450 \ud559\uc0dd\ub07c\ub9ac\ub294 \uacbd\uae30\ub97c \ud3bc\uce58\uc9c0 \uc54a\uc544\ub3c4 \ub204\uac00 \uc774\uae34\ub2e4\ub294 \uac83\uc744 \uc54c \uc218 \uc788\ub2e4\ub294 \uac83\uc774\ub2e4. \uc608\ub97c \ub4e4\uc5b4, \uc704\uc640 \uac19\uc740 \uadf8\ub798\ud504\uc5d0\uc11c 1\ubc88\uc740 2, 3\ubc88\uc744 \ud56d\uc0c1 \uc774\uae34\ub2e4\ub294 \ub73b\uc774\ub2e4. \ud558\uc9c0\ub9cc 1\ubc88\uacfc 4\ubc88\uc774 \uacbd\uae30\ud558\uba74 1\ubc88\uc774 \uc774\uae38 \uc218\ub3c4 \uc788\uace0 4\ubc88\uc774 \uc774\uae38 \uc218\ub3c4 \uc788\ub2e4.<\/p>\r\n<p>N\uba85\uc758 \ucc38\uac00\uc790\uc5d0 \ub300\ud55c \ucc9c\uc801 \uad00\uacc4\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c \uc6b0\uc2b9 \uac00\ub2a5\uc131\uc774 \uc788\ub294 \ud559\uc0dd\ub4e4\uc744 \uc54c \uc218 \uc788\ub2e4. \uc608\ub97c \ub4e4\uc5b4, \uc704\uc758 \uc608\uc5d0\uc11c 3\ubc88 \ud559\uc0dd\uc740 1\ubc88 \ud559\uc0dd\ud55c\ud14c \ud56d\uc0c1 \uc9c0\uc9c0\ub9cc 4\ubc88 \ud559\uc0dd\uacfc 1\ubc88 \ud559\uc0dd\uc774 \uacbd\uae30\ub97c \ud558\uc5ec 1\ubc88 \ud559\uc0dd\uc774 \ud0c8\ub77d\ud55c \ud6c4 3\ubc88 \ud559\uc0dd\uc774 2, 4\ubc88 \ud559\uc0dd\uc744 \ucc28\ub840\ub300\ub85c \uc774\uae30\uace0 \uc6b0\uc2b9\ud560 \uc218 \uc788\uae30 \ub54c\ubb38\uc5d0 \uc6b0\uc2b9 \uac00\ub2a5\uc131\uc774 \uc788\ub294 \ud559\uc0dd\uc774\ub2e4.<\/p>\r\n<p>\ubb38\uc81c\ub294 N\uba85\uc758 \ucc38\uac00\uc790\uc5d0 \ub300\ud55c \ucc9c\uc801 \uad00\uacc4\uac00 \uc8fc\uc5b4\uc9c0\uba74 \uc6b0\uc2b9 \uac00\ub2a5\uc131\uc774 \uc788\ub294 \ud559\uc0dd\ub4e4\uc744 \ubaa8\ub450 \uad6c\ud558\ub294 \uac83\uc774\ub2e4. <\/p>","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ucc38\uac00\uc790 \uc218 N(1&le;N&le;100,000)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ub2e4\uc74c N\uac1c\uc758 \uc904\uc5d0 \ucc9c\uc801\uad00\uacc4\uac00 \uc8fc\uc5b4\uc9c0\ub294\ub370 i+1\ubc88\uc9f8 \uc904\uc5d0\ub294 i\ubc88\uc9f8 \ud559\uc0dd\uc774 \ud56d\uc0c1 \uc774\uae30\ub294 \ud559\uc0dd\uc758 \uc218 \uc640 \uc774 \ud559\uc0dd\ub4e4\uc758 \ubc88\ud638\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc99d\uac00\ud558\ub294 \uc21c\uc11c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. (\ub2e8, \uc790\uae30 \uc790\uc2e0\uc774 \ucc9c\uc801\uc778 \uacbd\uc6b0\ub294 \uc5c6\ub2e4.) \ucc9c\uc801 \uad00\uacc4\uc758 \ucd1d \uc218\ub294 1,000,000\uc744 \ub118\uc9c0 \uc54a\ub294\ub2e4.<\/p>","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc6b0\uc2b9 \uac00\ub2a5\uc131\uc774 \uc788\ub294 \ud559\uc0dd \uc218 w\uc640 \uc774 \ud559\uc0dd\ub4e4\uc758 \ubc88\ud638\ub97c \uc624\ub984\ucc28\uc21c\uc73c\ub85c \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ud558\uc5ec \ucd9c\ub825\ud55c\ub2e4.<\/p>","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"1608","problem_lang":"1","title":"The Tournament","description":"<p>The International X-Game Federation organises a tournament in which programmes that play this game participate. &nbsp;programmes numbered from &nbsp;to &nbsp;take part in the competition. The rules of the tournament are as follows: while there remains more than one programme in the tournament, two of them (distinct) are randomly chosen to play a game. The defeated one (there are no draws in the X-Game) drops out of the tournament and the whole procedure is repeated. The sole programme which stays in the tournament after all &nbsp;games have been played is the winner.<\/p>\r\n\r\n<p>The federation has a table of results of previous tournaments. It is known, that the programmes play deterministically (i.e. in repeatable fashion) and in exactly the same way as in previous tournaments. So, if two programmes have already played one against another then their next game will end with the same result. If, however, they have never played against each other, the outcome of the game cannot be predicted - both have a chance of winning. The federation would like to know a list of all programmes which have a chance of winning the tournament.<\/p>\r\n\r\n<p>Write a programme which:<\/p>\r\n\r\n<ul>\r\n\t<li>reads from the standard input the number of participating programmes and the table of results of their previous games,<\/li>\r\n\t<li>determines all programmes which have a chance of winning the tournament,<\/li>\r\n\t<li>writes the outcome to the standard output.<\/li>\r\n<\/ul>\r\n","input":"<p>The first line of the input contains an integer n, 1 &le; n &le; 100 000. The next n lines contain the table of results of previous games: (i+1)st line contains an integer ki, 0 &le; ki &le; n, followed by ki numbers of programmes, not equal to i, in increasing order - those are the numbers of programmes, with which the programme i has previously won. The numbers in lines are separated by single spaces. The number of all known results of previous games does not exceed 1 000 000.<\/p>\r\n","output":"<p>The first and only line of the standard output should contain the number w of programmes which have a chance of winning the tournament, followed by w numbers identifying those programmes, in increasing order. The numbers should be separated by single spaces.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","hint":"<p><img alt=\"\" src=\"\/JudgeOnline\/upload\/201007\/rrr.PNG\" style=\"height:160px; width:124px\" \/><\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]