A tree is an undirected connected graph with no cycles. You are given a tree having (n) vertices. Each vertex (i) has an integer value (a_i) written on it. For any two vertices (u) and (v) ((u \ne v)), define (p(u, v)) as the product of the values written on the vertices lying on the unique simple path(^{\text{∗}}) from (u) to (v). An unordered triplet of three distinct vertices (\{u, v, w\}) is called good if and only if: (p(u,v)\cdot p(v,w)\cdot p(w,u)) is a perfect square . Determine the number of good unordered triplets in the given tree. (^{\text{∗}})A simple path from the vertex (u) to vertex (v) is a sequence of distinct vertices (u = x_0, x_1, \ldots, x_k = v) such that there exists an edge between vertices (x_{i-1}) and (x_i) for all (1 \le i \le k). The first line contains an integer (t) ((1 \le t \le 10^4)) — the number of test cases. The description of each test case follows. Each test case begins with an integer (n) ((3 \le n \le 2\cdot 10^5)) — the number of vertices. The second line contains (n) integers (a_1,a_2,\dots,a_n) ((1 \le a_i \le 10^6)) — the integer values written on the vertices. Each of the next (n-1) lines contains two integers (u,v) ((1 \le u,v \le n)), denoting an edge of the tree. It is guaranteed that the edges form a tree. It is guaranteed that the sum of (n) over all the test cases does not exceed (2\cdot 10^5). For each test case output the number of good triplets in the tree. For the first test case, all the unordered triplets of three distinct vertices are good: (\{1, 2, 3\}) (\{1, 2, 4\}) (\{1, 2, 5\}) (\{1, 3, 4\}) (\{1, 3, 5\}) (\{1, 4, 5\}) (\{2, 3, 4\}) (\{2, 3, 5\}) (\{2, 4, 5\}) (\{3, 4, 5\})