#include using namespace std; #include using namespace atcoder; //using mint = modint998244353; using mint = modint1000000007; using ll = long long; using ld = long double; using pll = pair; using tlll = tuple; constexpr ll INF = 1LL << 60; template bool chmin(T& a, T b) {if (a > b) {a = b; return true;} return false;} template bool chmax(T& a, T b) {if (a < b) {a = b; return true;} return false;} ll safemod(ll A, ll M) {return (A % M + M) % M;} ll divfloor(ll A, ll B) {if (B < 0) {return divfloor(-A, -B);} return (A - safemod(A, B)) / B;} ll divceil(ll A, ll B) {if (B < 0) {return divceil(-A, -B);} return divfloor(A + B - 1, B);} template void unique(vector &V) {V.erase(unique(V.begin(), V.end()), V.end());} template void sortunique(vector &V) {sort(V.begin(), V.end()); V.erase(unique(V.begin(), V.end()), V.end());} #define FINALANS(A) do {cout << (A) << '\n'; exit(0);} while (false) template void printvec(vector &V) {int _n = V.size(); for (int i = 0; i < _n; i++) cout << V[i] << (i == _n - 1 ? '\n' : ' ');} template void printvect(vector &V) {for (auto v : V) cout << v << '\n';} template void printvec2(vector> &V) {for (auto &v : V) printvec(v);} int main() { ll N; cin >> N; vector A(N); for (ll i = 0; i < N; i++) { cin >> A.at(i); } vector cnt(N, 0); for (auto a : A) { if (a < N) cnt.at(a)++; } vector dp(2, vector(N + 1, mint(0))); dp.at(0).at(0) = 1; for (ll i = 0; i < N; i++) { ll pi = i % 2, ni = 1 - pi; for (ll j = 0; j <= N; j++) { dp.at(ni).at(j) = 0; } for (ll j = 0; j < N; j++) { dp.at(ni).at(j + 1) += cnt.at(i) * dp.at(pi).at(j); dp.at(ni).at(j) += dp.at(pi).at(j); } } vector fac(N + 1); fac.at(0) = 1; for (ll i = 1; i <= N; i++) { fac.at(i) = fac.at(i - 1) * i; } mint ans = 0; for (ll j = 0; j <= N; j++) { mint tmp = (j % 2 == 0 ? 1 : -1) * dp.at(N % 2).at(j) * fac.at(N - j); ans += tmp; } cout << ans.val() << endl; }