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 $i \lt j \lt k$, 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 $2^{64}$.

共有 $n$ 名玩家，编号从 $0$ 到 $n-1$，每名玩家有一个等级。第 $i$ 名玩家的等级为 $i$。

玩家可以组队：每支队伍必须恰好由三名玩家组成，且队内任意两名玩家之间不能存在冲突。队伍的等级按如下算法计算：设队内三名玩家的等级分别为 $i$、$j$、$k$，且满足 $i \lt j \lt k$，则该队伍的等级为 $A \cdot i + B \cdot j + C \cdot k$。

现给出所有存在冲突的玩家对信息。请计算所有可能的有效队伍的等级之和，并对 $2^{64}$ 取模。

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 $v_i$ ($0 \le u_i, v_i \lt n, u_i \neq v_i$) — pair of conflicting players.

It's guaranteed that each unordered pair of players appears in the input file no more than once.

第一行包含两个以空格分隔的整数 $n$ 和 $m$（$3 \le n \le 2 \cdot 10^5$，$0 \le m \le 2 \cdot 10^5$）—— 分别表示玩家数量和冲突对的数量。

第二行包含三个以空格分隔的整数 $A$、$B$ 和 $C$（$1 \le A, B, C \le 10^6$）—— 团队排名计算所用的系数。

接下来的 $m$ 行中，每行包含两个以空格分隔的整数 $u_i$ 和 $v_i$（$0 \le u_i, v_i \lt n$，且 $u_i \neq v_i$）—— 表示一对存在冲突的玩家。

保证输入文件中每个无序玩家对至多出现一次。

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

输出一个整数——所有可能队伍的排名总和对 $2^{64}$ 取模的结果。

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}.

在第一个例子中，所有 $4$ 支队伍均有效，即三元组：{0, 1, 2}、{0, 1, 3}、{0, 2, 3}、{1, 2, 3}。

在第二个例子中，有效的队伍为：{0, 2, 3}、{1, 2, 3}。

在第三个例子中，有效的队伍为：{0, 1, 2}、{0, 1, 4}、{0, 1, 5}、{0, 2, 4}、{0, 2, 5}、{1, 2, 3}、{1, 2, 4}、{1, 2, 5}。