#include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; class range {private: struct I{int x;int operator*(){return x;}bool operator!=(I& lhs){return x 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 namespace solver { int n; vector vs; void read() { cin >> n; vs.resize(n); for (int i : range(n)) cin >> vs[i]; } double dp[101][101][101]; double run() { dp[0][0][0] = 0; for (int zer : range(n + 1)) for (int one : range(n + 1)) for (int two : range(n + 1)) { int comp = n - (zer + one + two); if (comp < 0) continue; if (comp == n) continue; double d = 1.0; if (zer > 0) d += dp[zer - 1][one + 1][two] * zer / n; if (one > 0) d += dp[zer][one - 1][two + 1] * one / n; if (two > 0) d += dp[zer][one][two - 1] * two / n; d /= 1.0 - 1.0 * comp / n; dp[zer][one][two] = d; dump(zer << " " << one << " " << two << " => " << d) } int zer = 0, one = 0, two = 0; for (int i : range(n)) { if (vs[i] == 0) zer++; if (vs[i] == 1) one++; if (vs[i] == 2) two++; } return dp[zer][one][two]; } } int main(int argc, char** argv) { cout << fixed << setprecision(12); int testcase = 1; if (argc > 1) testcase = atoi(argv[1]); while (testcase--) { solver::read(); } cout << solver::run() << endl; }