#include #include #include #include using mint = atcoder::modint998244353; int ChoosePair(const int n) { return n * (n + 1) / 2; } // // Õ(n^3) 時間? mint Solve(const std::vector>& tree) { const int n = tree.size(); const mint denominator = mint(ChoosePair(n)).inv(); const auto F = [](const mint& probability) -> mint { return probability * (2 - probability) * (1 - probability).pow(2).inv(); }; const auto G = [&denominator, F](const int num1, const int num2) -> mint { return F(num1 * num2 * denominator); }; std::vector subtree(n); // 部分木の大きさ const auto CalcSubtree = [&tree, &subtree]( auto CalcSubtree, const int parent, const int vertex) -> void { subtree[vertex] = 1; for (const int neighborhood : tree[vertex]) { if (neighborhood != parent) { CalcSubtree(CalcSubtree, vertex, neighborhood); subtree[vertex] += subtree[neighborhood]; } } }; // 最後の操作前にそのパスが白く塗られている期待値を求める mint ans = 0; const auto dfs = [&tree, n, &denominator, G, &subtree, &ans]( auto dfs, const int root, const int child_of_root, const int parent, const int vertex, const int distance, int bad_choice) -> void { for (const int neighborhood_of_vertex : tree[vertex]) { if (neighborhood_of_vertex != parent) { bad_choice += ChoosePair(subtree[neighborhood_of_vertex]); } } if (distance < n - 1 && root < vertex) { mint expected_value = G(n - subtree[child_of_root], subtree[vertex]); for (const int neighborhood_of_root : tree[root]) { if (neighborhood_of_root != child_of_root) { expected_value -= G(subtree[neighborhood_of_root], subtree[vertex]); } } for (const int neighborhood_of_vertex : tree[vertex]) { if (neighborhood_of_vertex != parent) { expected_value -= G(n - subtree[child_of_root], subtree[neighborhood_of_vertex]); } } for (const int neighborhood_of_root : tree[root]) { if (neighborhood_of_root == child_of_root) continue; for (const int neighborhood_of_vertex : tree[vertex]) { if (neighborhood_of_vertex == parent) continue; expected_value += G(subtree[neighborhood_of_root], subtree[neighborhood_of_vertex]); } } ans += expected_value * bad_choice * denominator; } for (const int neighborhood : tree[vertex]) { if (neighborhood != parent) { dfs(dfs, root, child_of_root, vertex, neighborhood, distance + 1, bad_choice - ChoosePair(subtree[neighborhood])); } } }; for (int root = 0; root < n; ++root) { CalcSubtree(CalcSubtree, -1, root); int bad_choice = 0; for (const int child : tree[root]) bad_choice += ChoosePair(subtree[child]); for (const int child : tree[root]) { dfs(dfs, root, child, root, child, 1, bad_choice - ChoosePair(subtree[child])); } // パス P = (root) のとき mint expected_value = F(1 - bad_choice * denominator); for (const int child : tree[root]) { expected_value -= G(n - subtree[child], subtree[child]); } const int children_num = tree[root].size(); for (int i = 0; i < children_num; ++i) { for (int j = i + 1; j < children_num; ++j) { expected_value += G(subtree[tree[root][i]], subtree[tree[root][j]]); } } ans += expected_value * bad_choice * denominator; } return ans; } int main() { constexpr int kMaxT = 100000, kMaxN = 40000; int t; std::cin >> t; assert(1 <= t && t <= kMaxT); while (t--) { int n; std::cin >> n; assert(2 <= n && n <= kMaxN); std::vector> tree(n); for (int i = 0; i < n - 1; ++i) { int u, v; std::cin >> u >> v; assert(1 <= u && u <= n && 1 <= v && v <= n); --u; --v; tree[u].emplace_back(v); tree[v].emplace_back(u); } std::cout << Solve(tree).val() << '\n'; } return 0; }