CF1795G.Removal Sequences

You are given a simple undirected graph, consisting of $n$ vertices and $m$ edges. The vertices are numbered from $1$ to $n$. The $i$-th vertex has a value $a_i$ written on it.

You will be removing vertices from that graph. You are allowed to remove vertex $i$ only if its degree is equal to $a_i$. When a vertex is removed, all edges incident to it are also removed, thus, decreasing the degree of adjacent non-removed vertices.

A valid sequence of removals is a permutation $p_1, p_2, \dots, p_n$ $(1 \le p_i \le n)$ such that the $i$-th vertex to be removed is $p_i$, and every removal is allowed.

A pair $(x, y)$ of vertices is nice if there exist two valid sequences of removals such that $x$ is removed before $y$ in one of them and $y$ is removed before $x$ in the other one.

Count the number of nice pairs $(x, y)$ such that $x \lt y$.

给你一个简单的无向图，包含 $n$ 个顶点和 $m$ 条边。顶点编号为 $1$ 到 $n$。第 $i$ 个顶点上写有一个值 $a_i$。

你将从该图中逐个删除顶点。仅当顶点 $i$ 的度数等于 $a_i$ 时，才允许删除它。当一个顶点被删除时，所有与之关联的边也会被同时删除，从而使得与其相邻且尚未被删除的顶点的度数减少。

一个合法的删除序列是一个排列 $p_1, p_2, \dots, p_n$（其中 $1 \le p_i \le n$），表示第 $i$ 个被删除的顶点是 $p_i$，且每次删除操作均满足上述条件。

若存在两个合法的删除序列，使得在其中一个序列中顶点 $x$ 在 $y$ 之前被删除，而在另一个序列中 $y$ 在 $x$ 之前被删除，则称顶点对 $(x, y)$ 是友好的（nice）。

请计算满足 $x \lt y$ 的友好对 $(x, y)$ 的数量。

The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of testcases.

The first line of each testcase contains two integers $n$ and $m$ ($1 \le n \le 10^5$; $0 \le m \le \min(10^5, \frac{n \cdot (n - 1)}{2})$) — the number of vertices and the number of edges of the graph.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le n - 1$) — the degree requirements for each removal.

Each of the next $m$ lines contains two integers $v$ and $u$ ($1 \le v, u \le n$; $v \neq u$) — the description of an edge.

The graph doesn't contain any self-loops or multiple edges.

The sum of $n$ over all testcases doesn't exceed $10^5$. The sum of $m$ over all testcases doesn't exceed $10^5$.

Additional constraint on the input: there always exists at least one valid sequence of removals.

第一行包含一个整数 $t$（$1 \le t \le 10^4$）——测试用例的数量。

每个测试用例的第一行包含两个整数 $n$ 和 $m$（$1 \le n \le 10^5$；$0 \le m \le \min(10^5, \frac{n \cdot (n - 1)}{2})$）——图中顶点数和边数。

第二行包含 $n$ 个整数 $a_1, a_2, \dots, a_n$（$0 \le a_i \le n - 1$）——每次移除操作对应的度数要求。

接下来的 $m$ 行，每行包含两个整数 $v$ 和 $u$（$1 \le v, u \le n$；$v \neq u$）——一条边的描述。

该图不含自环或重边。

所有测试用例的 $n$ 之和不超过 $10^5$；所有测试用例的 $m$ 之和不超过 $10^5$。

输入的额外约束：总存在至少一个合法的移除序列。

For each testcase, print a single integer — the number of nice pairs of vertices.

对于每个测试用例，输出一个整数——“好”顶点对的数量。