#include #define mp make_pair #define mt make_tuple #define pb push_back #define rep(i,n) for(int i=0;i<(n);i++) using namespace std; typedef long long ll; typedef unsigned long long ull; typedef pair pii; typedef pair pll; const int INF=1<<29; const double EPS=1e-9; const int MOD = 100000007; const int dx[]={1,0,-1,0},dy[]={0,-1,0,1}; int N; double dp[110][110][110]; double memo(int two, int one, int zero){ if (dp[two][one][zero] >= 0){ return dp[two][one][zero]; } if (two == 0 && one == 0 && zero == 0){ return 0.0; } double res = N * 1.0 / (two + one + zero); if (two > 0){ res += memo(two - 1, one, zero) * two / (two + one + zero); } if (one > 0){ res += memo(two + 1, one -1, zero) * one / (two + one + zero); } if (zero > 0){ res += memo(two, one + 1, zero - 1) * zero / (two + one + zero); } return dp[two][one][zero] = res; } int main(){ cin >> N; int two,one,zero; two = one = zero = 0; for (int i = 0; i < N; i++){ int x; cin >> x; if (x == 0){ zero++; }else if(x == 1){ one++; }else if(x == 2){ two++; } } memset(dp, -1, sizeof(dp)); printf("%.20lf\n", memo(two, one, zero)); }