Yousef has a rooted tree(^{\text{∗}}) consisting of exactly (n) vertices, which is rooted at vertex (1). You would like to give Yousef an array (a) of length (n), where each (a_i) ((1 \le i \le n)) can either be (1) or (2) . Let (s_u) denote the sum of (a_v) where vertex (v) is in the subtree(^{\text{†}}) of vertex (u). Yousef considers the tree special if all the values in (s) are pairwise distinct (i.e., all subtree sums are unique). Your task is to help Yousef count the number of different arrays (a) that result in the tree being special . Two arrays (b) and (c) are different if there exists an index (i) such that (b_i \neq c_i). As the result can be very large, you should print it modulo (10^9 + 7). (^{\text{∗}})A tree is a connected undirected graph with (n - 1) edges. (^{\text{†}})The subtree of a vertex (v) is the set of all vertices that pass through (v) on a simple path to the root. Note that vertex (v) is also included in the set. The first line contains an integer (t) ((1 \le t \le 10^4)) — the number of test cases. Each test case consists of several lines. The first line of the test case contains an integer (n) ((2 \le n \le 2 \cdot 10^5)) — the number of vertices in the tree. Then (n−1) lines follow, each of them contains two integers (u) and (v) ((1 \le u,v \le n, u \ne v)) which describe a pair of vertices connected by an edge. It is guaranteed that the given graph is a tree and has no loops or multiple edges. It is guaranteed that the sum of (n) over all test cases doesn't exceed (2 \cdot 10^5). For each test case, print one integer (x) — the number of different arrays (a) that result in the tree being special , modulo (10^9 + 7). The tree given in the fifth test case: