You are given a rooted tree(^{\text{∗}}) containing (n) vertices rooted at vertex (1). A pair of vertices ((u,v)) is called a good pair if (u) is not an ancestor(^{\text{†}}) of (v) and (v) is not an ancestor of (u). For any two vertices, (\text{dist}(u,v)) is defined as the number of edges on the unique simple path from (u) to (v), and (\text{lca}(u,v)) is defined as their lowest common ancestor . A function (f(u,v)) is defined as follows. If ((u,v)) is a good pair, (f(u,v)) is the number of distinct integer values (x) such that there exists a non-degenerate triangle (^{\text{‡}}) formed by side lengths (\text{dist}(u,\text{lca}(u,v))), (\text{dist}(v,\text{lca}(u,v))), and (x). Otherwise, (f(u,v)) is (0). You need to find the following value: ()\sum_{i = 1}^{n-1} \sum_{j = i+1}^n f(i,j).() (^{\text{∗}})A tree is a connected graph without cycles. A rooted tree is a tree where one vertex is special and called the root. (^{\text{†}})An ancestor of vertex (v) is any vertex on the simple path from (v) to the root, including the root, but not including (v). The root has no ancestors. (^{\text{‡}})A triangle with side lengths (a), (b), (c) is non-degenerate when (a+b > c), (a+c > b), (b+c > a). 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 3 \cdot 10^5)). Each of the next (n-1) lines contains two integers (u_i) and (v_i), denoting the two vertices connected by an edge ((1 \le u_i,v_i \le n), (u_i \neq v_i)). 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 (3 \cdot 10^5). For each test case, output the answer on a