G. Team Playerstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThere 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}.InputThe 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.OutputPrint single integer — the total sum of ranks over all possible teams modulo 2^{64}.ExamplesInput4 02 3 4Output64Input4 12 3 41 0Output38Input6 41 5 30 33 55 44 3Output164NoteIn 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}.
Input4 02 3 4
Output64
['combinatorics', '*2700']