CF985G Team Players

There are $ n $ players numbered from $ 0 $ to $ n-1 $ with ranks. The $ i $ -th player has rank $ i $ . Players can form teams: the team should consist of three players and no pair of players in the team should have a conflict. The rank of the team is calculated using the following algorithm: let $ i $ , $ j $ , $ k $ be the ranks of players in the team and $ i < j < k $ , then the rank of the team is equal to $ A \cdot i + B \cdot j + C \cdot k $ . You are given information about the pairs of players who have a conflict. Calculate the total sum of ranks over all possible valid teams modulo $ 2^{64} $ .

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In the first example all $ 4 $ teams are valid, i.e. triples: {0, 1, 2}, {0, 1, 3}, {0, 2, 3} {1, 2, 3}. In the second example teams are following: {0, 2, 3}, {1, 2, 3}. In the third example teams are following: {0, 1, 2}, {0, 1, 4}, {0, 1, 5}, {0, 2, 4}, {0, 2, 5}, {1, 2, 3}, {1, 2, 4}, {1, 2, 5}.