You are given a tree(^{\text{∗}}) with (n) vertices. Over time, each vertex (i) ((1 \le i \le n)) has a probability of (\frac{p_i}{q_i}) of falling. Determine the expected value of the number of unordered pairs(^{\text{†}}) of distinct vertices that become leaves(^{\text{‡}}) in the resulting forest(^{\text{§}}), modulo (998\,244\,353). Note that when vertex (v) falls, it is removed along with all edges connected to it. However, adjacent vertices remain unaffected by the fall of (v). (^{\text{∗}})A tree is a connected graph without cycles. (^{\text{†}})An unordered pair is a collection of two elements where the order in which the elements appear does not matter. For example, the unordered pair ((1, 2)) is considered the same as ((2, 1)). (^{\text{‡}})A leaf is a vertex that is connected to exactly one edge. (^{\text{§}})A forest is a graph without cycles Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first line of each test case contains a single integer (n) ((1 \le n \le 10^5)). The (i)-th line of the following (n) lines contains two integers (p_i) and (q_i) ((1 \le p_i < q_i < 998\,244\,353)). Each of the following (n - 1) lines contains two integers (u) and (v) ((1 \le u, v \le n), (u \neq v)) — the indices of the vertices connected by an edge. It is guaranteed that the given edges form a tree. It is guaranteed that the sum of (n) over all test cases does not exceed (10^5). For each test case, output a single integer — the expected value of the number of unordered pairs of distinct vertices that become leaves in the resulting forest modulo (998\,244\,353). Formally, let (M = 998\,244\,353). It can be shown that the exact answer can be expressed as an irreducible fraction (\frac{p}{q}), where (p)