#include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; auto range(int n) { return views::iota(0, n); } template ostream& operator<<(ostream& os, const pair& p){ return os << "{" << p.first << ", " << p.second << "}"; } template ostream& operator<<(ostream& os, const vector& obj) { os << "{"; for (const auto& e : obj) os << e << ", "; return os << "}"; } template ostream& operator<<(ostream& os, const set& obj) { os << "set{"; for (const auto& e : obj) os << e << ", "; return os << "}"; } template ostream& operator<<(ostream& os, const map& obj) { os << "map{"; for (const auto& e : obj) os << e << ", "; return os << "}"; } #ifdef ONLINE_JUDGE #define dump(expr) ; #else #define dump(expr) { cerr << "\033[33m#L" << __LINE__ << ": " << expr << "\033[39m" << endl; } #endif const int mod = 1000000007; struct mint { ll x; mint(ll x_ = 0) : x((x_ % mod + mod) % mod) {} mint operator-() const { return mint(-x); } mint &operator+=(const mint &a) { if ((x += a.x) >= mod) x -= mod; return *this; } mint &operator-=(const mint &a) { if ((x += mod - a.x) >= mod) x -= mod; return *this; } mint &operator*=(const mint &a) { (x *= a.x) %= mod; return *this; } mint operator+(const mint &a) const { mint res(*this); return res += a; } mint operator-(const mint &a) const { mint res(*this); return res -= a; } mint operator*(const mint &a) const { mint res(*this); return res *= a; } mint pow(ll t) const { if (!t) return 1; mint a = pow(t >> 1); a *= a; if (t & 1) a *= *this; return a; } mint inv() const { return pow(mod - 2); } mint &operator/=(const mint &a) { return (*this) *= a.inv(); } mint operator/(const mint &a) const { mint res(*this); return res /= a; } friend ostream &operator<<(ostream &os, const mint &m) { os << m.x; return os; } friend istream &operator>>(istream &is, mint &m) { is >> m.x; return is; } }; vector fact, invfact; void prepare(int n) { fact.resize(n + 1); invfact.resize(n + 1); fact[0] = 1; for (int i : range(n)) fact[i + 1] = fact[i] * (i + 1); for (int i : range(n + 1)) invfact[i] = fact[i].inv(); } mint combin(int n, int r) { if (r > n) return mint(0); return fact[n] * invfact[r] * invfact[n - r]; } ll solve() { int N; cin >> N; prepare(N); vector> dp(N + 1, vector(N + 1)); dp[0][0] = 1; for (int g : views::iota(1, N + 1)) for (int n : views::iota(1, N + 1)) for (int k : range(n)) { dp[g][n] += combin(n - 1, k) * dp[g - 1][n - 1 - k]; } dump(dp); mint res = 0; for (int g : range(N + 1)) for (int n : range(N + 1)) { if (dp[g][n].x) { dump(g << " " << n << " => " << dp[g][n] << " " << (mint(g) * (g - 1)).pow(N - n)); } res += dp[g][n] * combin(N, n) * (mint(g) * (g - 1)).pow(N - n); } dump(res); return res.x; } int main() { cout << fixed << setprecision(12); cout << solve() << endl; }