////////////////////////////// // Check before you submit. // #define _ATCODER_LIBRARY const long long MOD = 1e9+7; // const long long MOD = 998244353; ///////////////////////////// #include using namespace std; #include using namespace boost::multiprecision; #ifdef _ATCODER_LIBRARY #include using namespace atcoder; #endif // _ATCODER_LIBRARY const long long INF = 1LL << 60; const double PI = acos(-1); using ll = long long; using P = pair; #define FOR(i,a,b) for (ll i=(a);i<(ll)(b);++i) #define REP(i,n) FOR(i,0,n) #define ALL(v) (v).begin(),(v).end() #define SUM(v) accumulate(ALL(v),0ll) templateistream& operator>>(istream&i,vector&v){REP(j,v.size())i>>v[j];return i;} templatestring join(vector&v){stringstream s;REP(i,v.size())s<<' '<ostream& operator<<(ostream&o,vector&v){if(v.size())o<string join(vector>&vv){string s="\n";REP(i,vv.size())s+=join(vv[i])+"\n";return s;} templateostream& operator<<(ostream&o,vector>&vv){if(vv.size())o<istream& operator>>(istream&i,pair&v){return i>>v.first>>v.second;} templateostream& operator<<(ostream&o,pair&v){return o<T up(T a, T b){assert(b);return (a+b-1)/b;} templatebool eq(A const&... a){auto t={a...};assert(t.size());auto tar=*t.begin();for(const auto&e:t)if(tar!=e)return false;return true;} templatebool chmin(T &a, T b){if(a>b){a=b;return false;}return true;} templatebool chmax(T &a, T b){if(abool chmax(T &a, initializer_listl){return chmax(a,max(l));} templatebool chmin(T &a, initializer_listl){return chmin(a,min(l));} ////////////////////////////////////////////////////////////////// // My Library ////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////// // Contest Code ////////////////////////////////////////////////////////////////// ll N; double dp[110][110][110]; double solve(ll a, ll b, ll c) { if (dp[a][b][c] != -1) return dp[a][b][c]; ll d = N - (a + b + c); double res{(double)N/(N-d)}; if (a)res += solve(a-1, b+1, c)*a/(a+b+c); if (b)res += solve(a, b-1, c+1)*b/(a+b+c); if (c)res += solve(a, b, c-1)*c/(a+b+c); return dp[a][b][c] = res; } int main(int argc, char **argv) { init_init_init(); cin >> N; REP(a, 110)REP(b, 110)REP(c, 110) dp[a][b][c] = -1; dp[0][0][0] = 0; vector cnt(4, 0ll); REP(i, N) { ll a; cin >> a; cnt[min(3ll, a)]++; } double a = solve(cnt[0], cnt[1], cnt[2]); std::cout << a << std::endl; }