A11833. 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}.