// TLE 区間DP 苦行 #include #include #include #include #include using mint = atcoder::modint998244353; struct SubtreeSize { SubtreeSize(int n, const std::vector> &g) : _n(n), _par(_n, -1), _siz(_n, 1) { auto dfs = [&](auto dfs, int u, int p) -> int { _par[u] = p; for (int v : g[u]) if (v != p) { _siz[u] += dfs(dfs, v, u); } return _siz[u]; }; dfs(dfs, 0, -1); } int operator()(int u, int p) const { return _par[u] == p ? _siz[u] : _n - _siz[p]; } int t(int u, int ng1) const { return _n - (*this)(ng1, u); } int t(int u, int ng1, int ng2) const { return _n - (*this)(ng1, u) - (*this)(ng2, u); } private: int _n; std::vector _par, _siz; }; int edge_num(int n) { return (n * (n + 1)) >> 1; } int main() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); auto solve = [&]{ int n; std::cin >> n; std::vector> g(n); for (int i = 0; i < n - 1; ++i) { int u, v; std::cin >> u >> v; --u, --v; g[u].push_back(v); g[v].push_back(u); } const int m = edge_num(n); const mint inv_m = mint(m).inv(); SubtreeSize subtree_size { n, g }; std::vector ans_f(n, 0); for (int x = 0; x < n; ++x) { int u_x = edge_num(n); for (int y : g[x]) { u_x -= edge_num(subtree_size(y, x)); } ans_f[x] = m * mint(m - u_x).inv(); } std::vector> ans_g(n, std::vector(n)); std::vector> par(n, std::vector(n, -1)); // x, y std::deque> dq; for (int x = 0; x < n; ++x) { ans_g[x][x] = ans_f[x]; for (int y : g[x]) { par[x][y] = x; dq.emplace_back(x, y); } } while (dq.size()) { auto [x, z] = dq.front(); dq.pop_front(); std::vector Pxz; for (int a = z; a != -1; a = par[x][a]) { Pxz.push_back(a); } assert(Pxz.front() == z and Pxz.back() == x and Pxz.size() >= 2); const int l = Pxz.size(); auto get_t_z = [&](int idx) { return idx == 0 ? subtree_size.t(Pxz[idx], Pxz[idx + 1]) : idx == l - 1 ? subtree_size.t(Pxz[idx], Pxz[idx - 1]) : subtree_size.t(Pxz[idx], Pxz[idx - 1], Pxz[idx + 1]); }; for (int i = 0; i < l; ++i) { const int z2 = Pxz[i]; std::vector ng; if (i > 0) ng.push_back(Pxz[i - 1]); if (i + 1 < l) ng.push_back(Pxz[i + 1]); int u_z2 = 1; { int sum = 0; for (int nz : g[z2]) if (nz != ng.front() and nz != ng.back()) { int s_nz = subtree_size(nz, z2); u_z2 += sum * s_nz; sum += s_nz; } u_z2 += sum; } ans_g[x][z] += u_z2 * ans_f[z2]; const int t2 = get_t_z(i); for (int j = 0; j < i; ++j) { if (i == l - 1 and j == 0) continue; const int z1 = Pxz[j]; const int t1 = get_t_z(j); ans_g[x][z] += t1 * t2 * ans_g[z2][z1]; } } ans_g[x][z] = (1 + ans_g[x][z] * inv_m) * (1 - get_t_z(l - 1) * get_t_z(0) * inv_m).inv(); for (int y : g[z]) if (y != par[x][z]) { par[x][y] = z; dq.emplace_back(x, y); } } mint ans = 1; for (int x = 0; x < n; ++x) { for (int y = 0; y <= x; ++y) { ans += ans_g[x][y] * inv_m; } } std::cout << ans.val() << '\n'; }; int t; std::cin >> t; while (t --> 0) { solve(); } return 0; }