#include using namespace std; template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } return false; } // std::vector Declaration template vector make_v(size_t a) { return vector(a); } template auto make_v(size_t a, Ts... ts) { return vector(ts...))>(a, make_v(ts...)); } // std::vector Declaration and Initialization template vector make_vector(size_t a, T x) { return vector(a, x); } template auto make_vector(size_t a, U b, Ts... ts) { return vector(b,ts...))>(a, make_vector(b, ts...)); } // std::vector Input template istream& operator>>(istream& is, vector& v) { for (auto &e : v) is >> e; return is; } // std::vector Debug template ostream& operator<<(ostream& os, const vector& v) { os << "["; bool a = 1; for (auto e : v) { os << (a ? "" : " "); os << e; a = 0; } os << "]"; return os; } // std::array Debug template ostream& operator<<(ostream& os, const array& v) { os << "["; bool a = 1; for (auto e : v) { os << (a ? "" : " "); os << e; a = 0; } os << "]"; return os; } // std::deque Debug template ostream& operator<<(ostream& os, const deque& d) { os << "["; bool a = 1; for (auto e : d) { os << (a ? "" : " "); os << e; a = 0; } os << "]"; return os; } // std::pair Debug template ostream& operator<<(ostream& os, const pair& p) { os << "(" << p.first << " " << p.second << ")"; return os; } // std::set Debug template ostream& operator<<(ostream& os, const set& st) { os << "{"; bool a = 1; for (auto e : st) { os << (a ? "" : " "); os << e; a = 0; } os << "}"; return os; } // std::multiset Debug template ostream& operator<<(ostream& os, const multiset& st) { os << "{"; bool a = 1; for (auto e : st) { os << (a ? "" : " "); os << e; a = 0; } os << "}"; return os; } // std::map Debug template ostream& operator<<(ostream& os, const map& mp) { os << "{"; bool a = 1; for (auto e : mp) { os << (a ? "" : " "); os << e.first << ":" << e.second; a = 0; } os << "}"; return os; } // std::tuple Debug template void out(ostream& os, const Tuple& t){} template void out(ostream& os, const Tuple& t) { if (N) os << " "; os << get(t); out(os, t); } template ostream& operator<<(ostream& os, const tuple& t) { os << "("; out<0,tuple,Ts...>(os, t); os << ")"; return os; } // Debug #define DUMP(x) cerr<<#x<<" = "<<(x)< struct edge { int src, to; T cost; edge() {} edge(int to, T cost) : src(-1), to(to), cost(cost) {} edge(int src, int to, T cost) : src(src), to(to), cost(cost) {} friend ostream& operator<<(ostream& os, const edge& e) { return os << "(" << e.src << "->" << e.to << ":" << e.cost << ")"; } }; using LL = int64_t; #define fs first #define sc second template struct modint { using LL = int64_t; LL val; modint(LL val=0) : val(((val % mod) + mod) % mod) {} const modint operator+() const { return *this; } const modint operator-() const { return (-val + mod) % mod; } const modint inv() const { return pow(mod-2); } modint& operator+=(const modint& rhs) { (val += rhs.val) %= mod; return *this; } modint& operator-=(const modint& rhs) { return *this += -rhs; } modint& operator*=(const modint& rhs) { (val *= rhs.val) %= mod; return *this; } modint& operator/=(const modint& rhs) { return *this *= rhs.inv(); } const modint operator+(const modint& rhs) const { return modint(*this) += rhs; } const modint operator-(const modint& rhs) const { return modint(*this) -= rhs; } const modint operator*(const modint& rhs) const { return modint(*this) *= rhs; } const modint operator/(const modint& rhs) const { return modint(*this) /= rhs; } const modint pow(LL n) const { modint ret = 1, tmp = val; while (n > 0) { if (n & 1) ret *= tmp; tmp *= tmp; n >>= 1; } return ret; } bool operator==(const modint& rhs) const { return val == rhs.val; } bool operator!=(const modint& rhs) const { return !(*this == rhs); } friend const modint operator+(const LL& lhs, const modint& rhs) { return modint(lhs) + rhs; } friend const modint operator-(const LL& lhs, const modint& rhs) { return modint(lhs) - rhs; } friend const modint operator*(const LL& lhs, const modint& rhs) { return modint(lhs) * rhs; } friend const modint operator/(const LL& lhs, const modint& rhs) { return modint(lhs) / rhs; } friend bool operator==(const LL& lhs, const modint& rhs) { return modint(lhs) == rhs; } friend bool operator!=(const LL& lhs, const modint& rhs) { return modint(lhs) != rhs; } friend ostream& operator<<(ostream& os, const modint& a) { return os << a.val; } friend istream& operator>>(istream& is, modint& a) { LL tmp; is >> tmp; a = tmp; return is; } }; const int64_t MOD = 1e9+7; using Int = modint; int main() { cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(10); int n; cin >> n; map cnt; for (int i = 0; i < n; ++i) { int a; cin >> a; if (a >= n) continue; ++cnt[a]; } vector b; for (const auto& tp : cnt) b.push_back(tp.second); int m = b.size(); auto dp = make_v(2, n+1); dp[0][0] = 1; for (int i = 0; i < m; ++i) { dp[(i+1) & 1].assign(n+1, 0); for (int j = 0; j <= n; ++j) { dp[(i+1) & 1][j] += dp[i & 1][j]; if (j < n) dp[(i+1) & 1][j+1] += dp[i & 1][j] * b[i]; } } vector fact(n+1); fact[0] = 1; for (int i = 1; i <= n; ++i) { fact[i] = fact[i-1] * i; } Int ans = 0; for (int k = 0; k <= n; ++k) { ans += dp[m & 1][k] * fact[n-k] * (k & 1 ? -1 : 1); } cout << ans << endl; return 0; }