====== Monochromatic Triangles ======

===== 풀이 =====
  * [[ps:tutorial:부분그래프 세기#모두 연결되었거나, 모두 연결되어있지 않은 세 노드 세기]] 참고.
  * {{myicon>p4}} [[ps:problems:boj:8907]], {{myicon>p4}} [[ps:problems:boj:17275]] 도 동일한 문제이다.
  * 시간복잡도는 O(|E|).

===== 코드 =====
<dkpr py>
"""Solution code for "BOJ 8096. Monochromatic Triangles".

- Problem link: https://www.acmicpc.net/problem/8096
- Solution link: http://www.teferi.net/ps/problems/boj/8096

Tags: [math]
"""

import math
import sys
from teflib import graph as tgraph


def count_3_cycle_or_3_independent_set(graph):
    n = len(graph)
    degs = [len(neighbors) for neighbors in graph]
    invalid_set_count = sum(d * (n - 1 - d) for d in degs) // 2
    return math.comb(n, 3) - invalid_set_count


def main():
    n = int(sys.stdin.readline())
    m = int(sys.stdin.readline())
    graph = tgraph.create_graph_from_input(n, m)

    print(count_3_cycle_or_3_independent_set(graph))


if __name__ == '__main__':
    main()
</dkpr>

{{tag>BOJ ps:problems:boj:플래티넘_4}}