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문제

유명한 피타고라스의 정리와 유사한 형태의 피타고라스 기댓값 (Pythagorean Expectation)이 야구와 같은 스포츠 경기에 자주 사용된다. 피타고라스 기댓값은 빌 제임스(Bill James)에 의해 정의되었으며, 이 값은 특정 야구팀이 한 시즌 동안 얼마나 잘 했는지를 평가하는 지표 중 하나로 사용된다. 한 야구팀의 피타고라스 기댓값 \(W\)는 아래 식과 같이 정의된다.

\(W = \dfrac{S^2}{S^2 + A^2}\),

여기서 \(S\)는 해당 팀의 총 득점 수를, \(A\)는 해당 팀의 총 실점 수를 나타낸다.

이 기댓값을 실제 승률과 비교하여, 해당 팀이 한 시즌을 얼마나 잘 보냈는지 평가할 수 있다. 예를 들어, 한화 이글스는 2014 시즌에 619 득점과 889 실점을 했다. 즉, \(S\) = 619, \(A\) = 889이 되어, 한화 팀의 피타고라스 기댓값은 \(W\) = 6192/(6192 + 8892) = 0.326이 된다. KBO 규정에 따르면, 한 시즌당 한 팀은 128번의 경기를 해야 하므로, 한화는 0.326 ×128 = 41.728 경기에서는 승리했어야 한다. 실제 한화는 49경기에서 승리했기 때문에, 2014 시즌을 그리 나쁘지 않게 보냈음을 알 수 있다. 반면에 롯데 자이언츠는 \(S\) = 715이고, \(A\) = 719이 되어, \(W\) = 0.497이 된다. 따라서 0.497 ×128 = 63.616경기 이상을 이길 것으로 기대되었지만, 실제론 58경기만 승리했다. 결국, 롯데에게 2014년은 기대에 많이 못 미친 시즌이었음을 알 수 있다.

\(n\)개의 팀에 대한 기록이 주어지면, 이 기록으로부터 팀 별 피타고라스 기댓값을 계산한 후, 그 중 최대 기댓값과 최소 기댓값을 출력하는 프로그램을 작성하시오.

입력

입력 데이터는 표준입력을 사용한다. 입력은 T개의 테스트 데이터로 구성된다. 입력의 첫 번째 줄에는 입력 데이터의 수를 나타내는 정수 T가 주어진다. 각 테스트 데이터의 첫 줄에는 두 양의 정수 \(n\) (2 ≤ \(n\) ≤ 1,000)과 \(m\) (2 ≤ \(m\) ≤ 1,000)이 주어진다. 여기서, \(n\)은 팀 개수이며, \(m\)은 전체 경기 수이다. 다음의 \(m\)개의 줄에는 각 경기에 대한 정보가 주어진다. 하나의 경기는 네 개의 정수 \(a\), \(b\), \(p\), \(q\)로 주어지는데, 팀 a와 팀 b가 경기를 했고, 팀 a는 p득점을 팀 b는 q득점을 했다는 의미이다. 여기서, 1 ≤ \(a\) ≠ \(b\) ≤ \(n\)이며, \(p\)와 \(q\)는 모두 음이 아닌 20 이하의 정수이다. 하나의 테스트 데이터에서 팀 당 경기수가 반드시 같을 필요는 없다. 만약, 어떤 팀의 총 득점과 총 실점이 모두 0이라면, 그 팀의 기댓값은 0으로 정의한다.

출력

출력은 표준 출력을 사용한다. 각 테스트 데이터에 대해, 두 정수 값을 한 줄에 하나씩 출력해야 한다. 첫 번째 줄에는 최대 피타고라스 기댓값에 1,000을 곱한 값의 정수부분을 출력하고, 두 번째 줄에는 최소 피타고라스 기댓값에 1,000을 곱한 값의 정수부분을 출력한다.

예제 입력 1

2
3 5
1 2 3 5
1 3 10 1
1 2 0 7
2 3 9 3
3 2 4 5
4 6
1 2 0 11
1 3 17 13
1 4 17 1
2 3 7 12
2 4 19 17
3 4 17 0

예제 출력 1

871
100
753
103
[{"problem_id":"11070","problem_lang":"0","title":"\ud53c\ud0c0\uace0\ub77c\uc2a4 \uae30\ub313\uac12","description":"<p>\uc720\uba85\ud55c \ud53c\ud0c0\uace0\ub77c\uc2a4\uc758 \uc815\ub9ac\uc640 \uc720\uc0ac\ud55c \ud615\ud0dc\uc758 \ud53c\ud0c0\uace0\ub77c\uc2a4 \uae30\ub313\uac12 (Pythagorean Expectation)\uc774 \uc57c\uad6c\uc640 \uac19\uc740 \uc2a4\ud3ec\uce20 \uacbd\uae30\uc5d0 \uc790\uc8fc \uc0ac\uc6a9\ub41c\ub2e4. \ud53c\ud0c0\uace0\ub77c\uc2a4 \uae30\ub313\uac12\uc740 \ube4c \uc81c\uc784\uc2a4(Bill James)\uc5d0 \uc758\ud574 \uc815\uc758\ub418\uc5c8\uc73c\uba70, \uc774 \uac12\uc740 \ud2b9\uc815 \uc57c\uad6c\ud300\uc774 \ud55c \uc2dc\uc98c \ub3d9\uc548 \uc5bc\ub9c8\ub098 \uc798 \ud588\ub294\uc9c0\ub97c \ud3c9\uac00\ud558\ub294 \uc9c0\ud45c \uc911 \ud558\ub098\ub85c \uc0ac\uc6a9\ub41c\ub2e4. \ud55c \uc57c\uad6c\ud300\uc758 \ud53c\ud0c0\uace0\ub77c\uc2a4 \uae30\ub313\uac12 \\(W\\)\ub294 \uc544\ub798 \uc2dd\uacfc \uac19\uc774 \uc815\uc758\ub41c\ub2e4.<\/p>\r\n\r\n<p style=\"text-align:center\">\\(W = \\dfrac{S^2}{S^2 + A^2}\\),<\/p>\r\n\r\n<p>\uc5ec\uae30\uc11c \\(S\\)\ub294 \ud574\ub2f9 \ud300\uc758 \ucd1d \ub4dd\uc810 \uc218\ub97c, \\(A\\)\ub294 \ud574\ub2f9 \ud300\uc758 \ucd1d \uc2e4\uc810 \uc218\ub97c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n\r\n<p>\uc774 \uae30\ub313\uac12\uc744 \uc2e4\uc81c \uc2b9\ub960\uacfc \ube44\uad50\ud558\uc5ec, \ud574\ub2f9 \ud300\uc774 \ud55c \uc2dc\uc98c\uc744 \uc5bc\ub9c8\ub098 \uc798 \ubcf4\ub0c8\ub294\uc9c0 \ud3c9\uac00\ud560 \uc218 \uc788\ub2e4. \uc608\ub97c \ub4e4\uc5b4, \ud55c\ud654 \uc774\uae00\uc2a4\ub294 2014 \uc2dc\uc98c\uc5d0 619 \ub4dd\uc810\uacfc 889 \uc2e4\uc810\uc744 \ud588\ub2e4. \uc989, \\(S\\)&nbsp;= 619, \\(A\\) = 889\uc774 \ub418\uc5b4, \ud55c\ud654 \ud300\uc758 \ud53c\ud0c0\uace0\ub77c\uc2a4 \uae30\ub313\uac12\uc740 \\(W\\) = 619<sup>2<\/sup>\/(619<sup>2<\/sup> + 889<sup>2<\/sup>) = 0.326\uc774 \ub41c\ub2e4. KBO \uaddc\uc815\uc5d0 \ub530\ub974\uba74, \ud55c \uc2dc\uc98c\ub2f9 \ud55c \ud300\uc740 128\ubc88\uc758 \uacbd\uae30\ub97c \ud574\uc57c \ud558\ubbc0\ub85c, \ud55c\ud654\ub294 0.326 &times;128 = 41.728&nbsp;\uacbd\uae30\uc5d0\uc11c\ub294 \uc2b9\ub9ac\ud588\uc5b4\uc57c \ud55c\ub2e4. \uc2e4\uc81c \ud55c\ud654\ub294 49\uacbd\uae30\uc5d0\uc11c \uc2b9\ub9ac\ud588\uae30 \ub54c\ubb38\uc5d0, 2014 \uc2dc\uc98c\uc744 \uadf8\ub9ac \ub098\uc058\uc9c0 \uc54a\uac8c \ubcf4\ub0c8\uc74c\uc744 \uc54c \uc218 \uc788\ub2e4. \ubc18\uba74\uc5d0 \ub86f\ub370 \uc790\uc774\uc5b8\uce20\ub294 \\(S\\) = 715\uc774\uace0, \\(A\\) = 719\uc774 \ub418\uc5b4, \\(W\\)&nbsp;= 0.497\uc774 \ub41c\ub2e4. \ub530\ub77c\uc11c 0.497 &times;128 = 63.616\uacbd\uae30 \uc774\uc0c1\uc744 \uc774\uae38 \uac83\uc73c\ub85c \uae30\ub300\ub418\uc5c8\uc9c0\ub9cc, \uc2e4\uc81c\ub860 58\uacbd\uae30\ub9cc \uc2b9\ub9ac\ud588\ub2e4. \uacb0\uad6d, \ub86f\ub370\uc5d0\uac8c 2014\ub144\uc740 \uae30\ub300\uc5d0 \ub9ce\uc774 \ubabb \ubbf8\uce5c \uc2dc\uc98c\uc774\uc5c8\uc74c\uc744 \uc54c \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\\(n\\)\uac1c\uc758 \ud300\uc5d0 \ub300\ud55c \uae30\ub85d\uc774 \uc8fc\uc5b4\uc9c0\uba74, \uc774 \uae30\ub85d\uc73c\ub85c\ubd80\ud130 \ud300 \ubcc4 \ud53c\ud0c0\uace0\ub77c\uc2a4 \uae30\ub313\uac12\uc744 \uacc4\uc0b0\ud55c \ud6c4, \uadf8 \uc911 \ucd5c\ub300 \uae30\ub313\uac12\uacfc \ucd5c\uc18c \uae30\ub313\uac12\uc744 \ucd9c\ub825\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uc785\ub825 \ub370\uc774\ud130\ub294 \ud45c\uc900\uc785\ub825\uc744 \uc0ac\uc6a9\ud55c\ub2e4. \uc785\ub825\uc740 T\uac1c\uc758 \ud14c\uc2a4\ud2b8 \ub370\uc774\ud130\ub85c \uad6c\uc131\ub41c\ub2e4. \uc785\ub825\uc758 \uccab \ubc88\uc9f8 \uc904\uc5d0\ub294 \uc785\ub825 \ub370\uc774\ud130\uc758 \uc218\ub97c \ub098\ud0c0\ub0b4\ub294 \uc815\uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ub370\uc774\ud130\uc758 \uccab \uc904\uc5d0\ub294 \ub450 \uc591\uc758 \uc815\uc218 \\(n\\) (2 &le; \\(n\\) &le; 1,000)\uacfc \\(m\\) (2 &le; \\(m\\) &le; 1,000)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \uc5ec\uae30\uc11c, \\(n\\)\uc740 \ud300 \uac1c\uc218\uc774\uba70, \\(m\\)\uc740&nbsp;\uc804\uccb4 \uacbd\uae30 \uc218\uc774\ub2e4. \ub2e4\uc74c\uc758 \\(m\\)\uac1c\uc758 \uc904\uc5d0\ub294 \uac01 \uacbd\uae30\uc5d0 \ub300\ud55c \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ud558\ub098\uc758 \uacbd\uae30\ub294 \ub124 \uac1c\uc758 \uc815\uc218 \\(a\\), \\(b\\), \\(p\\), \\(q\\)\ub85c \uc8fc\uc5b4\uc9c0\ub294\ub370, \ud300 a\uc640 \ud300 b\uac00 \uacbd\uae30\ub97c \ud588\uace0, \ud300 a\ub294 p\ub4dd\uc810\uc744 \ud300 b\ub294 q\ub4dd\uc810\uc744 \ud588\ub2e4\ub294 \uc758\ubbf8\uc774\ub2e4. \uc5ec\uae30\uc11c, 1 &le; \\(a\\) &ne; \\(b\\) &le; \\(n\\)\uc774\uba70, \\(p\\)\uc640 \\(q\\)\ub294 \ubaa8\ub450 \uc74c\uc774 \uc544\ub2cc 20 \uc774\ud558\uc758 \uc815\uc218\uc774\ub2e4. \ud558\ub098\uc758 \ud14c\uc2a4\ud2b8 \ub370\uc774\ud130\uc5d0\uc11c \ud300 \ub2f9 \uacbd\uae30\uc218\uac00 \ubc18\ub4dc\uc2dc \uac19\uc744 \ud544\uc694\ub294 \uc5c6\ub2e4. \ub9cc\uc57d, \uc5b4\ub5a4 \ud300\uc758 \ucd1d \ub4dd\uc810\uacfc \ucd1d \uc2e4\uc810\uc774 \ubaa8\ub450 0\uc774\ub77c\uba74, \uadf8 \ud300\uc758 \uae30\ub313\uac12\uc740 0\uc73c\ub85c \uc815\uc758\ud55c\ub2e4.<\/p>\r\n","output":"<p>\ucd9c\ub825\uc740 \ud45c\uc900 \ucd9c\ub825\uc744 \uc0ac\uc6a9\ud55c\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ub370\uc774\ud130\uc5d0 \ub300\ud574, \ub450 \uc815\uc218 \uac12\uc744 \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \ucd9c\ub825\ud574\uc57c \ud55c\ub2e4. \uccab \ubc88\uc9f8 \uc904\uc5d0\ub294 \ucd5c\ub300 \ud53c\ud0c0\uace0\ub77c\uc2a4 \uae30\ub313\uac12\uc5d0 1,000\uc744 \uacf1\ud55c \uac12\uc758 \uc815\uc218\ubd80\ubd84\uc744 \ucd9c\ub825\ud558\uace0, \ub450 \ubc88\uc9f8 \uc904\uc5d0\ub294 \ucd5c\uc18c \ud53c\ud0c0\uace0\ub77c\uc2a4 \uae30\ub313\uac12\uc5d0 1,000\uc744 \uacf1\ud55c \uac12\uc758 \uc815\uc218\ubd80\ubd84\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"11070","problem_lang":"1","title":"Pythagorean Expectation","description":"<p>A formula similar to the famous Pythagorean Theorem has been used in baseball. This is called Pythagorean Expectation, invented by Bill James. This expectation is used to estimate how many games a baseball team should have won during a season. The Pythagorean Expectation \\(W\\) for a baseball team is defined as follows.<\/p>\r\n\r\n<p>\\(W = \\frac{S^2}{S^2 + A^2}\\),<\/p>\r\n\r\n<p>where \\(S\\) is the number of runs the team scored, and \\(A\\) is the number of runs the team allowed. The formula name comes from the resemblance to the Pythagorean Theorem.&nbsp;<\/p>\r\n\r\n<p>This expectation empirically tells how the baseball team actually performs by comparing the real winning ratio. For example, Hanwha Eagles has scored 619 runs, but allowed 889 runs during 2014 season, that is, \\(S\\) = 619, \\(A\\) = 889, so \\(W\\) = 619<sup>2<\/sup>\/(619<sup>2<\/sup> + 889<sup>2<\/sup>) = 0.326. Since each team plays 128 games according to the KBO rule, Eagles should have won 0.326 &times; 128 = 41.728 games. But Eagles actually won 49 games, showing they were not bad at all. For Lotte Giants with \\(S\\) = 715 and \\(A\\) = 719, \\(W\\) = 0.497, so they should have won 0.497 &times; 128 = 63.616 games. Since Giants actually won 58 games, one may say that they performed a bit poor for the season.&nbsp;<\/p>\r\n\r\n<p>Given records of the games between baseball teams, you are to write the largest and the smallest Pythagorean expectations of the teams.<\/p>\r\n","input":"<p>Your program is to read from standard input. The input consists of T test cases. The number of test cases T is given in the first line of the input. Each test case starts with a line containing two integers, \\(n\\) (2 &le; \\(n\\) &le; 1,000) and \\(m\\) (2 &le; \\(m\\) &le; 1,000), where \\(n\\) is the number of baseball teams, and \\(m\\) is the total number of games between \\(n\\) teams. In the following \\(m\\) lines, a record for each game is given line by line. Each record is represented by four numbers \\(a\\), \\(b\\), \\(p\\), \\(q\\), separated by a single space, which means team \\(a\\) has played against team \\(b\\), and team \\(a\\) has scored \\(p\\) runs and team \\(b\\) has scored \\(q\\) runs. Note that 1 &le; \\(a\\) &ne; \\(b\\) &le; \\(n\\), and \\(p\\) and \\(q\\) are non-negative integers no more than 20. Note that teams in a test case may have different number of games. If a team has no scored and allowed runs, then its expectation value becomes zero.<\/p>\r\n","output":"<p>Your program is to write to standard output. Print two integers for each test case. The first line should contain the integer part of the value, the largest Pythagorean Expectation of the teams times 1,000. The second line should contain the integer part of the value, the smallest Pythagorean Expectation of the teams times 1,000.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]