#include #include #include #include using mint = atcoder::modint998244353; int ChoosePair(const int n) { return n * (n + 1) / 2; } // // Õ(n^2) 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(); }; 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]; } } }; mint ans = 0; // 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 const auto dfs = [&tree, n, &denominator, F, &subtree, &ans]( auto dfs, const int root, const int child_of_root, const int bad_close_to_root, const int bad_of_root, const int parent, const int vertex, const int distance, const int bad_choice) -> void { int bad_close_to_vertex = 0; for (const int child : tree[vertex]) { if (child != parent) bad_close_to_vertex += ChoosePair(subtree[child]); } if (root < vertex) { // 一度だけカウントしたい mint end_probability = 0; if (distance == 1) { assert(bad_choice == 0); if (distance < n - 1) { end_probability += bad_close_to_root + bad_close_to_vertex; } end_probability -= bad_close_to_root + ChoosePair(subtree[vertex]); end_probability -= bad_of_root + bad_close_to_vertex; } else { if (distance < n - 1) { end_probability += bad_choice + bad_close_to_root + bad_close_to_vertex; } end_probability -= bad_choice + bad_close_to_root + ChoosePair(subtree[vertex]); end_probability -= bad_choice + bad_of_root + bad_close_to_vertex; end_probability += bad_choice + bad_of_root + ChoosePair(subtree[vertex]); } end_probability *= denominator; ans += F((n - subtree[child_of_root]) * subtree[vertex] * denominator) * end_probability; } for (const int child : tree[vertex]) { if (child != parent) { const int tmp = ChoosePair(subtree[child]); dfs(dfs, root, child_of_root, bad_close_to_root, bad_of_root, vertex, child, distance + 1, bad_choice + bad_close_to_vertex - ChoosePair(subtree[child])); } } }; 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, bad_choice - ChoosePair(subtree[child]), ChoosePair(n - subtree[child]), root, child, 1, 0); } // パス P = (root) のとき ans += F(1 - bad_choice * denominator) * 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; }