#include #include #include #include using mint = atcoder::modint998244353; int ChoosePair(const int n) { return n * (n + 1) / 2; } 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 parent(n, -1); std::vector subtree(n, 1); // 根を頂点 1 とする部分木の大きさ const auto CalcSubtree = [&tree, &parent, &subtree]( auto CalcSubtree, const int vertex) -> void { for (const int neighborhood : tree[vertex]) { if (neighborhood != parent[vertex]) { parent[neighborhood] = vertex; CalcSubtree(CalcSubtree, neighborhood); subtree[vertex] += subtree[neighborhood]; } } }; CalcSubtree(CalcSubtree, 0); mint ans = 0; // 長さ 0 のパス for (int i = 0; i < n; ++i) { int num_of_path = 0; for (const int neighborhood : tree[i]) { num_of_path += ChoosePair(neighborhood == parent[i] ? n - subtree[i] : subtree[neighborhood]); } ans += F(1 - num_of_path * denominator) * num_of_path * denominator; } // 長さ 1 のパス for (int i = 0; i < n; ++i) { for (const int j : tree[i]) { if (j == parent[i]) continue; ans += F((n - subtree[j]) * subtree[j] * denominator) * (-ChoosePair(n - subtree[j]) - ChoosePair(subtree[j])) * 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; }