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문제

동호는 월드 고등학교의 학생이다. 동호는 학교에서 N개의 시험을 봤다. 시험 점수는 Ti와 Pi로 주어진다. Ti는 i번째 시험에서 동호가 받은 점수를 의미하고, Pi는 i번째 시험의 토탈 점수를 의미한다.

이제 이 N개의 점수를 가지고 성적을 매겨야 하는데 성적은 Ti들의 합을 Pi들의 합으로 나눈 값을 의미한다. 만약에 동호가 1/2, 5/9, 3/8, 4/10, 1/3 의 점수를 얻었다면 (Ti/Pi의 형식) 동호가 받을 성적은 1+5+3+4+1/2+9+8+10+3 = 14/32 ≒ 0.44가 될 것이다.

그런데 동호의 담임 선생님은 그냥 이렇게 점수를 주면 동호의 성적이 너무 형편없기 때문에 동호가 본 N개의 시험 중, Ti를 Pi로 나눈 값, 즉 백분율이 작은 D개의 시험을 빼서 N-D개의 시험에 대해서만 성적을 합산하려 한다. 예를 들어 위에서 D가 1일 경우에는 1/3이 가장 작기 때문에 동호의 성적은 1/3을 뺀 1/2, 5/9, 3/8, 4/10을 더한 1+5+3+4/ 2+9+8+10 = 13/29 ≒ 0.45가 된다.

그런데 동호는 이러한 선생님의 선택에 반발을 하였다. 어차피 D개의 성적을 뺄 거면 다른 것을 빼지 왜 백분율이 작은 것을 빼냐는 것이다. 만약에 D가 1일 경우 1/3을 빼지 않고 3/8을 빼면 점수가 11/24 ≒ 0.46이 되어 위의 경우보다 점수가 더 높게 된다는 것이다.

동호의 담임선생님은 점수를 올려준다는데도 이에 반발한 동호에게 매우 화가 났다. 그래서 동호의 담임선생님은 즉석에서 다음과 같은 문제를 동호에게 내 주었다. 동호의 시험 점수가 주어져 있을 때, 동호의 이론이 성립하는 D를 모두 구하라는 것이다. 즉, 백분율이 작은 D개를 빼는 것 보다 다른 D개를 빼서 점수를 더 높이는 것이 가능한 D를 모두 구하라는 것이다. 동호는 매우 당황하였다. 점수를 올리려다가 큰 난관에 부딪힌 것이다. 여러분은 동호를 도와서 위의 조건은 만족하는 D를 모두 구하는 프로그램을 작성하여야 한다.

입력

첫째 줄에 동호가 시험을 본 개수 N(1≤N≤5,000, 단 마지막 데이터의 경우에 한해서 N=50,000이다). 그리고 두 번째 줄부터 N+1번째 줄까지 N개의 줄에 걸쳐 Pi와 Ti가 (0 ≤ Ti ≤ Pi ≤ 40,000  0<Pi) 공백을 사이에 두고 주어진다.

출력

첫 줄에 가능한 D의 개수 K(0≤K≤N) 를 출력한다. 그리고 두 번째 줄부터 K+1번째 줄까지 가능한 D를 모두 출력한다.

예제 입력 1

5
1 2
5 9
3 8
4 10
1 3

예제 출력 1

2
1
2
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Ti\ub294 i\ubc88\uc9f8 \uc2dc\ud5d8\uc5d0\uc11c \ub3d9\ud638\uac00 \ubc1b\uc740 \uc810\uc218\ub97c \uc758\ubbf8\ud558\uace0, Pi\ub294 i\ubc88\uc9f8 \uc2dc\ud5d8\uc758 \ud1a0\ud0c8 \uc810\uc218\ub97c \uc758\ubbf8\ud55c\ub2e4.<\/p><p>\uc774\uc81c \uc774 N\uac1c\uc758 \uc810\uc218\ub97c \uac00\uc9c0\uace0 \uc131\uc801\uc744 \ub9e4\uaca8\uc57c \ud558\ub294\ub370 \uc131\uc801\uc740 Ti\ub4e4\uc758 \ud569\uc744 Pi\ub4e4\uc758 \ud569\uc73c\ub85c \ub098\ub208 \uac12\uc744 \uc758\ubbf8\ud55c\ub2e4. \ub9cc\uc57d\uc5d0 \ub3d9\ud638\uac00 1\/2, 5\/9, 3\/8, 4\/10, 1\/3 \uc758 \uc810\uc218\ub97c \uc5bb\uc5c8\ub2e4\uba74 (Ti\/Pi\uc758 \ud615\uc2dd) \ub3d9\ud638\uac00 \ubc1b\uc744 \uc131\uc801\uc740 1+5+3+4+1\/2+9+8+10+3 = 14\/32 \u2252 0.44\uac00 \ub420 \uac83\uc774\ub2e4.<\/p><p>\uadf8\ub7f0\ub370 \ub3d9\ud638\uc758 \ub2f4\uc784 \uc120\uc0dd\ub2d8\uc740 \uadf8\ub0e5 \uc774\ub807\uac8c \uc810\uc218\ub97c \uc8fc\uba74 \ub3d9\ud638\uc758 \uc131\uc801\uc774 \ub108\ubb34 \ud615\ud3b8\uc5c6\uae30 \ub54c\ubb38\uc5d0 \ub3d9\ud638\uac00 \ubcf8 N\uac1c\uc758 \uc2dc\ud5d8 \uc911, Ti\ub97c Pi\ub85c \ub098\ub208 \uac12, \uc989 \ubc31\ubd84\uc728\uc774 \uc791\uc740 D\uac1c\uc758 \uc2dc\ud5d8\uc744 \ube7c\uc11c N-D\uac1c\uc758 \uc2dc\ud5d8\uc5d0 \ub300\ud574\uc11c\ub9cc \uc131\uc801\uc744 \ud569\uc0b0\ud558\ub824 \ud55c\ub2e4. \uc608\ub97c \ub4e4\uc5b4 \uc704\uc5d0\uc11c D\uac00 1\uc77c \uacbd\uc6b0\uc5d0\ub294 1\/3\uc774 \uac00\uc7a5 \uc791\uae30 \ub54c\ubb38\uc5d0 \ub3d9\ud638\uc758 \uc131\uc801\uc740 1\/3\uc744 \ube80 1\/2, 5\/9, 3\/8, 4\/10\uc744 \ub354\ud55c 1+5+3+4\/ 2+9+8+10 = 13\/29 \u2252 0.45\uac00 \ub41c\ub2e4.<\/p><p>\uadf8\ub7f0\ub370 \ub3d9\ud638\ub294 \uc774\ub7ec\ud55c \uc120\uc0dd\ub2d8\uc758 \uc120\ud0dd\uc5d0 \ubc18\ubc1c\uc744 \ud558\uc600\ub2e4. \uc5b4\ucc28\ud53c D\uac1c\uc758 \uc131\uc801\uc744 \ube84 \uac70\uba74 \ub2e4\ub978 \uac83\uc744 \ube7c\uc9c0 \uc65c \ubc31\ubd84\uc728\uc774 \uc791\uc740 \uac83\uc744 \ube7c\ub0d0\ub294 \uac83\uc774\ub2e4. \ub9cc\uc57d\uc5d0 D\uac00 1\uc77c \uacbd\uc6b0 1\/3\uc744 \ube7c\uc9c0 \uc54a\uace0 3\/8\uc744 \ube7c\uba74 \uc810\uc218\uac00 11\/24 \u2252 0.46\uc774 \ub418\uc5b4 \uc704\uc758 \uacbd\uc6b0\ubcf4\ub2e4 \uc810\uc218\uac00 \ub354 \ub192\uac8c \ub41c\ub2e4\ub294 \uac83\uc774\ub2e4.<\/p><p>\ub3d9\ud638\uc758 \ub2f4\uc784\uc120\uc0dd\ub2d8\uc740 \uc810\uc218\ub97c \uc62c\ub824\uc900\ub2e4\ub294\ub370\ub3c4 \uc774\uc5d0 \ubc18\ubc1c\ud55c \ub3d9\ud638\uc5d0\uac8c \ub9e4\uc6b0 \ud654\uac00 \ub0ac\ub2e4. \uadf8\ub798\uc11c \ub3d9\ud638\uc758 \ub2f4\uc784\uc120\uc0dd\ub2d8\uc740 \uc989\uc11d\uc5d0\uc11c \ub2e4\uc74c\uacfc \uac19\uc740 \ubb38\uc81c\ub97c \ub3d9\ud638\uc5d0\uac8c \ub0b4 \uc8fc\uc5c8\ub2e4. \ub3d9\ud638\uc758 \uc2dc\ud5d8 \uc810\uc218\uac00 \uc8fc\uc5b4\uc838 \uc788\uc744 \ub54c, \ub3d9\ud638\uc758 \uc774\ub860\uc774 \uc131\ub9bd\ud558\ub294 D\ub97c \ubaa8\ub450 \uad6c\ud558\ub77c\ub294 \uac83\uc774\ub2e4. \uc989, \ubc31\ubd84\uc728\uc774 \uc791\uc740 D\uac1c\ub97c \ube7c\ub294 \uac83 \ubcf4\ub2e4 \ub2e4\ub978 D\uac1c\ub97c \ube7c\uc11c \uc810\uc218\ub97c \ub354 \ub192\uc774\ub294 \uac83\uc774 \uac00\ub2a5\ud55c D\ub97c \ubaa8\ub450 \uad6c\ud558\ub77c\ub294 \uac83\uc774\ub2e4. \ub3d9\ud638\ub294 \ub9e4\uc6b0 \ub2f9\ud669\ud558\uc600\ub2e4. \uc810\uc218\ub97c \uc62c\ub9ac\ub824\ub2e4\uac00 \ud070 \ub09c\uad00\uc5d0 \ubd80\ub52a\ud78c \uac83\uc774\ub2e4. \uc5ec\ub7ec\ubd84\uc740 \ub3d9\ud638\ub97c \ub3c4\uc640\uc11c \uc704\uc758 \uc870\uac74\uc740 \ub9cc\uc871\ud558\ub294 D\ub97c \ubaa8\ub450 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc5ec\uc57c \ud55c\ub2e4.","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ub3d9\ud638\uac00 \uc2dc\ud5d8\uc744 \ubcf8 \uac1c\uc218 N(1&le;N&le;5,000, \ub2e8 \ub9c8\uc9c0\ub9c9 \ub370\uc774\ud130\uc758 \uacbd\uc6b0\uc5d0 \ud55c\ud574\uc11c N=50,000\uc774\ub2e4). \uadf8\ub9ac\uace0 \ub450 \ubc88\uc9f8 \uc904\ubd80\ud130 N+1\ubc88\uc9f8 \uc904\uae4c\uc9c0 N\uac1c\uc758 \uc904\uc5d0 \uac78\uccd0 Pi\uc640 Ti\uac00 (0 &le; Ti &le; Pi &le; 40,000&nbsp; 0&lt;Pi) \uacf5\ubc31\uc744 \uc0ac\uc774\uc5d0 \ub450\uace0 \uc8fc\uc5b4\uc9c4\ub2e4. ","output":"<p>\uccab \uc904\uc5d0 \uac00\ub2a5\ud55c D\uc758 \uac1c\uc218 K(0&le;K&le;N) \ub97c \ucd9c\ub825\ud55c\ub2e4. \uadf8\ub9ac\uace0 \ub450 \ubc88\uc9f8 \uc904\ubd80\ud130 K+1\ubc88\uc9f8 \uc904\uae4c\uc9c0 \uac00\ub2a5\ud55c D\ub97c \ubaa8\ub450 \ucd9c\ub825\ud55c\ub2e4.","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"1859","problem_lang":"1","title":"Cow School","description":"<p>Bessy is going to school and doing well. She has taken N (1 &lt;= N &lt;= 5000 -- except one case where 1 &lt;= N &lt;= 50,000) tests and recorded the scores (T_i points out of P_i points for test i; 0 &lt;= T_i &lt;= P_i &lt; 40,000; 0 &lt; P_i) as this task&#39;s input.<\/p>\r\n\r\n<p>Her teacher will drop the D tests with the lowest percentage (T_i\/P_i) before calculating Bessie&#39;s final grade (which is the sum of the remaining test score points over the sum of the remaining total test points). Bessy is good at math and quickly realizes that this does not benefit her as much as it might.<\/p>\r\n\r\n<p>To prove her point, Bessy wants to find all values of D for which she could have ended up with a higher grade by choosing to drop different tests than the teacher would have. Help her by finding and printing all values of D for which this is possible.<\/p>\r\n\r\n<p>Bessy has noted that, amazingly, she has never scored the same percentage on two different tests.<\/p>\r\n","input":"<p>* Line 1: A single integer, N<\/p>\r\n\r\n<p>* Lines 2..N+1: Line i+1 contains two space-separated integers: T_i and P_i<\/p>\r\n","output":"<p>* Line 1: A single integer K (0 &lt;= K &lt;= N) that is the number of values of D for which Bessy could have ended up with a higher grade by dropping a different set of D tests than the teacher.<\/p>\r\n\r\n<p>* Lines 2..K+1: The values of D for which this is true, in ascending numerical order.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]