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} $ .

The first line contains two space-separated integers $ n $ and $ m $ ( $ 3 \le n \le 2 \cdot 10^5 $ , $ 0 \le m \le 2 \cdot 10^5 $ ) — the number of players and the number of conflicting pairs. The second line contains three space-separated integers $ A $ , $ B $ and $ C $ ( $ 1 \le A, B, C \le 10^6 $ ) — coefficients for team rank calculation. Each of the next $ m $ lines contains two space-separated integers $ u_i $ and $ v_i $ ( $ 0 \le u_i, v_i < n, u_i \neq v_i $ ) — pair of conflicting players. It's guaranteed that each unordered pair of players appears in the input file no more than once.

Print single integer — the total sum of ranks over all possible teams modulo $ 2^{64} $ .

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}.