G. Removal Sequencestime limit per test4 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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 < y.InputThe 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.OutputFor each testcase, print a single integer — the number of nice pairs of vertices.ExampleInput
43 21 0 12 31 23 31 2 01 22 31 35 63 0 2 1 01 24 14 23 42 35 11 00Output
1
0
4
0

43 21 0 12 31 23 31 2 01 22 31 35 63 0 2 1 01 24 14 23 42 35 11 00
1 0 4 0 
['bitmasks', 'dfs and similar', 'graphs', '*2700']