#include #include #include template struct Edge { int src, dst; Cost cost; Edge(int src = -1, int dst = -1, Cost cost = 1) : src(src), dst(dst), cost(cost){}; bool operator<(const Edge& e) const { return this->cost < e.cost; } bool operator>(const Edge& e) const { return this->cost > e.cost; } }; template struct Graph { std::vector>> graph; Graph(int n = 0) : graph(n) {} void span(bool direct, int src, int dst, Cost cost = 1) { graph[src].emplace_back(src, dst, cost); if (!direct) graph[dst].emplace_back(dst, src, cost); } std::vector>& operator[](int v) { return graph[v]; } std::vector> operator[](int v) const { return graph[v]; } int size() const { return graph.size(); } }; template struct ModInt { using lint = long long; int val; // constructor ModInt(lint v = 0) : val(v % MOD) { if (val < 0) val += MOD; }; // unary operator ModInt operator+() const { return ModInt(val); } ModInt operator-() const { return ModInt(MOD - val); } ModInt inv() const { return this->pow(MOD - 2); } // arithmetic ModInt operator+(const ModInt& x) const { return ModInt(*this) += x; } ModInt operator-(const ModInt& x) const { return ModInt(*this) -= x; } ModInt operator*(const ModInt& x) const { return ModInt(*this) *= x; } ModInt operator/(const ModInt& x) const { return ModInt(*this) /= x; } ModInt pow(lint n) const { auto x = ModInt(1); auto b = *this; while (n > 0) { if (n & 1) x *= b; n >>= 1; b *= b; } return x; } // compound assignment ModInt& operator+=(const ModInt& x) { if ((val += x.val) >= MOD) val -= MOD; return *this; } ModInt& operator-=(const ModInt& x) { if ((val -= x.val) < 0) val += MOD; return *this; } ModInt& operator*=(const ModInt& x) { val = lint(val) * x.val % MOD; return *this; } ModInt& operator/=(const ModInt& x) { return *this *= x.inv(); } // compare bool operator==(const ModInt& b) const { return val == b.val; } bool operator!=(const ModInt& b) const { return val != b.val; } // I/O friend std::istream& operator>>(std::istream& is, ModInt& x) noexcept { return is >> x.val; } friend std::ostream& operator<<(std::ostream& os, const ModInt& x) noexcept { return os << x.val; } }; template std::vector bfs(const Graph& graph, int s) { std::vector dist(graph.size(), -1); dist[s] = 0; std::queue que; que.push(s); while (!que.empty()) { int v = que.front(); que.pop(); for (const auto& e : graph[v]) { if (dist[e.dst] != -1) continue; dist[e.dst] = dist[v] + e.cost; que.push(e.dst); } } return dist; } constexpr int MOD = 1e9 + 7; using mint = ModInt; void solve() { int n; std::cin >> n; Graph<> graph(n); for (int i = 0; i < n - 1; ++i) { int u, v; std::cin >> u >> v; graph.span(false, --u, --v); } mint ans = 0; auto ds = bfs(graph, 0); for (auto d : ds) ans += mint(d + 1).inv(); for (int i = 1; i <= n; ++i) ans *= i; std::cout << ans << std::endl; } int main() { std::cin.tie(nullptr); std::ios::sync_with_stdio(false); solve(); return 0; }