#include #define EPS 1e-9 #define INF 1070000000LL #define MOD 1000000007LL #define fir first #define foreach(it,X) for(auto it=(X).begin();it!=(X).end();it++) #define numa(x,a) for(auto x: a) #define ite iterator #define mp make_pair #define rep(i,n) rep2(i,0,n) #define rep2(i,m,n) for(int i=m;i<(n);i++) #define pb push_back #define pf push_front #define sec second #define sz(x) ((int)(x).size()) #define ALL( c ) (c).begin(), (c).end() #define gcd(a,b) __gcd(a,b) #define mem(x,n) memset(x,n,sizeof(x)) #define endl "\n" using namespace std; template void deploy(std::ostream &os, const TUPLE &tuple){} template void deploy(std::ostream &os, const TUPLE &t){ os << (POS == 0 ? "" : ", ") << get(t); deploy(os, t); } template std::ostream& operator<<(std::ostream &os, std::pair &p){ os << "(" << p.first <<", " << p.second <<")";return os; } template std::ostream& operator<<(std::ostream &os, std::vector &v){ int remain = v.size(); os << "{"; for(auto e: v) os << e << (--remain == 0 ? "}" : ", "); return os; } template std::ostream& operator<<(std::ostream &os, std::set &v){ int remain = v.size(); os << "{"; for(auto e: v) os << e << (--remain == 0 ? "}" : ", "); return os; } template std::ostream& operator<<(std::ostream &os, std::map &mp){ int remain = mp.size(); os << "{"; for(auto e: mp) os << "(" << e.first << " -> " << e.second << ")" << (--remain == 0 ? "}" : ", "); return os; } #define DEBUG1(var0) { std::cerr << (#var0) << "=" << (var0) << endl; } #define DEBUG2(var0, var1) { std::cerr << (#var0) << "=" << (var0) << ", ";DEBUG1(var1); } #define DEBUG3(var0, var1, var2) { std::cerr << (#var0) << "=" << (var0) << ", ";DEBUG2(var1,var2); } #define DEBUG4(var0, var1, var2, var3) { std::cerr << (#var0) << "=" << (var0) << ", ";DEBUG3(var1,var2,var3); } using ll = long long; int N; int nums[110]; double memo[110][110][110]; double dp_go(int zero, int one, int two){ if (zero == 0 && one == 0 && two == 0) { return 0; } if (memo[zero][one][two] >= 0) { return memo[zero][one][two]; } double ret = (double) N / (zero + one + two); if (zero >= 1) { ret += dp_go(zero - 1, one + 1, two) * ((double) zero / (zero + one + two)); } if (one >= 1) { ret += dp_go(zero, one - 1, two + 1) * ((double) one / (zero + one + two)); } if (two >= 1) { ret += dp_go(zero, one , two - 1) * ((double) two / (zero + one + two)); } return memo[zero][one][two] = ret; } int main() { cin.tie(0); ios_base::sync_with_stdio(0); cin >> N; int needs[4] = {0}; rep(i,N){ cin >> nums[i]; needs[min(3,nums[i])] += 1; } rep(i,105){ rep(j,105){ rep(k,105){ memo[i][j][k] = -1; } } } cout << fixed << setprecision(10) << dp_go(needs[0],needs[1],needs[2]) << endl; return 0; }