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문제

어느 행성에 N개의 작은 부족들이 살고 있다. 편의상 1부터 N까지 번호를 부여하자.

  • 임의의 서로 다른 두 부족은 서로 동맹 관계이거나 서로 적대 관계이다. 이 관계는 대칭적이다. 즉, 부족 A는 부족 B를 동맹이라 생각하나 B는 A를 적이라 생각하는 경우는 없다.
  • 부족 A와 부족 B가 동맹이고, 부족 B와 부족 C가 동맹이라도 부족 A와 부족 C가 적대 관계일 수 있다.
  • 임의의 서로 다른 세 부족에 대하여, 세 부족이 서로 동맹 관계인 경우를 "삼자 동맹 관계"라 하고, 세 부족이 서로 적대 관계인 경우를 "삼자 적대 관계"라 하자.

이 때, N개의 부족 내의 서로 다른 "삼자 동맹 관계"와 "삼자 적대 관계"들을 전부 합한 개수를 구하라.

예를 들어 N = 5이고 부족1-부족2, 부족1-부족3, 부족4-부족5가 서로 동맹 관계, 나머지 부족 쌍은 모두 적대 관계라고 가정하자. 이 경우 (2, 3, 4)와 (2, 3, 5) 가 "삼자 적대 관계"를 만족하고, "삼자 동맹 관계"는 없기 때문에 답은 2가 된다.

다른 예로 N = 5이고 부족1-부족2, 부족2-부족3, 부족1-부족3이 동맹인 경우 (1, 2, 3)은 "삼자 동맹 관계"이고, (1, 4, 5), (2, 4, 5), (3, 4, 5)는 "삼자 적대 관계"이기 때문에 답은 4가 된다.

입력

첫 줄에 테스트 케이스의 수 T가 주어진다 (1 ≤ T ≤ 10).

각 테스트 케이스 첫 줄에 N, M이 공백으로 구분 되어 주어진다.

다음 M줄에 걸쳐서 한 줄에 두 개의 정수 x, y가 주어지는데 이는 x와 y가 동맹임을 나타낸다.

입력으로 주어지는 동맹 관계는 언제나 1 ≤ x < y ≤ N을 만족하고, 같은 부족 쌍이 여러 번 주어지는 경우는 없다.

입력으로 주어지지 않은 부족 쌍은 적대관계라고 가정한다.

출력

각 테스트 케이스에 대해 한 줄에 동맹-반동맹 계수를 출력한다.

서브태스크 1 (4점)

  • 3 ≤ N ≤ 200
  • 1 ≤ M ≤ min(1,000, N × (N-1)/2)

서브태스크 2 (13점)

  • 3 ≤ N ≤ 5,000
  • 1 ≤ M ≤ min(1,000,000, N × (N-1)/2)

예제 입력 1

3
3 1
1 2
5 3
1 2
2 3
1 3
5 3
1 2
1 3
4 5

예제 출력 1

0
4
2
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These relationships are symmetric.<\/li>\r\n\t<li>Note that even if tribe A and B are allies and B and C are allies, tribe A and C can be hostile to each other.<\/li>\r\n\t<li>For three different tribes, if all of them are in an alliance, we call them as in &quot;3-way alliance&quot;; Similarly, if all of them are in hostility, we call them as in &quot;3-way hostility&quot;.<\/li>\r\n<\/ul>\r\n\r\n<p>Given the relationships between N tribes, return the sum of all of the 3-way alliances and 3-way hostilities.<\/p>\r\n\r\n<p>For instance, let N = 5 and (1, 2), (1, 3), and (4, 5) represent 3 alliance relationships (all other pairs are pairwise enemies). In this case (2, 3, 4) and (2, 3, 5) are &quot;3-way hostility&quot;, and there is no &quot;3-way alliance&quot;. Hence the answer&nbsp;is 2.<\/p>\r\n\r\n<p>In another example, let N = 5 and (1, 2), (2, 3), and (1, 3) represent 3 alliance relationships (again, all others are pairwise enemies). In this case, (1, 2, 3) is a &quot;3-way alliance&quot; and (1, 4, 5), (2, 4, 5), and (3, 4, 5) are &quot;3-way hostility&quot;. The answer is 4.&nbsp;<\/p>\r\n","input":"<p>The first line will contain the number of test cases, T (1 &le;&nbsp;T &le; 10).<\/p>\r\n\r\n<p>For each test case, the first line will contain N and M separated by a whitespace.<\/p>\r\n\r\n<p>For the next M lines, each line will contain two integers x and y such that tribes x and y are allies. You can assume that 1 &le;&nbsp;x &lt; y &le;&nbsp;N for all M lines, and no duplicate pairs will be provided in the input. <strong>Assume that all pairs of tribes that are not given in the input are pairwise enemies.&nbsp;<\/strong><\/p>\r\n","output":"<p>For each test case, output the 3-way AE Number in a single line.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\uc601\uc5b4","subtask1":"<ul>\r\n\t<li>3 &le; N &le; 200<\/li>\r\n\t<li>1 &le; M &le; min(1,000, N &times; (N-1)\/2)<\/li>\r\n<\/ul>\r\n","subtask2":"<ul>\r\n\t<li>3 &le; N &le; 5,000<\/li>\r\n\t<li>1 &le; M &le; min(1,000,000, N &times; (N-1)\/2)<\/li>\r\n<\/ul>\r\n"}]

채점

  • 예제는 채점하지 않는다.