#include <iostream>
#include <iomanip>
#include <fstream>
#include <string>
#include <array>
#include <vector>
#include <deque>
#include <list>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <stack>
#include <queue>
#include <bitset>
#include <tuple>
#include <cmath>
#include <complex>
#include <algorithm>
#include <utility>
#include <regex>
#include <cstdint>
#include <numeric>
#include <functional>
#include <cassert>

using namespace std;
using ll = int64_t;
using ull = uint64_t;

constexpr ll INF = 1000000000;/* 1e+9a */
namespace utils{

    class Repeater{
        int st;
        int ed;
        int d;
    public:
        class rep_iterator{
            int i; int d;
        public:
            rep_iterator(int x, int pd) :i(x), d(pd) {}

            int& operator*(){ return i; }
            bool operator==(const rep_iterator& k) const { return i == k.i; }
            bool operator!=(const rep_iterator& k) const { return i != k.i; }
            rep_iterator& operator++(){ i+=d; return *this; }
        };

        explicit Repeater(int N) :st(0), ed(N), d(1) {}
        Repeater(int b, int e) :st(b), ed(e), d(1) {if(st > ed){ st--; ed--; d = -1; } }

        rep_iterator begin() const{ return rep_iterator(st, d); }
        rep_iterator end() const{ return rep_iterator(ed, d); }

    };

    template<class T, class Compare> using p_queue = priority_queue<T, vector<T>, Compare>;
    template<class T> using min_queue = p_queue<T, greater<T>>;
    template<class T> using max_queue = p_queue<T, less<T>>;

    template<class T> bool min_update(T& X, const T& A){ if(X > A) {X = A; return true;} return false; }
    template<class T> bool max_update(T& X, const T& A){ if(X < A) {X = A; return true;} return false; }
#define ALL(x) begin(x), end(x)
#define rALL(x) rbegin(x), rend(x)
}
using namespace utils;

struct hash_triple {
    typedef size_t result_type;
    size_t operator()(const tuple<int, int, int>& t) const {
        return hash<long long>()
                (get<0>(t) *500 + get<1>(t) * 250000 + get<2>(t));
    }
};

class solver{

public:
     unordered_map<tuple<int, int, int>, double,
            hash_triple> dp;
    double dfs(int x, int y, int z, int N){
        if(dp.count(make_tuple(x, y, z))) return dp[make_tuple(x, y, z)];

        double A = x + y + z;
        if(A == 0) return 0;
        double dx = (x > 0 ? dfs(x-1, y, z, N)  * x / A : 0);
        double dy = (y > 0 ? dfs(x+1, y-1, z, N)  * y / A : 0);
        double dz = (z > 0 ? dfs(x, y+1, z-1, N) * z / A : 0);
        return dp[make_tuple(x, y, z)] = dx + dy + dz + N/A;

    }

};
void sub_main(istream &is) {
    ll N;
    is >> N;
    if(!is) return;
    int x, y, z;
    x = y = z = 0;
    for (int i = 0; i < N; ++i) {
        int t; is >> t;
        if(t == 1) x++;
        else if(t == 2) y++;
        else z++;
    } // end i


    cout << solver().dfs(x, y, z, N)<< endl;

}

int main(int argc, char *argv[]) {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << setprecision(16) << scientific;
#ifdef DEBUG
    string test_cases = "test_J.txt";
    cerr << "DEBUG MODE" <<  endl;
    cerr << test_cases << " -->" << endl;
    auto fs = fstream(test_cases, fstream::in);
    int lp = 0;
    while(fs) {
        lp++;
        cout << lp <<  "#------\n";
        sub_main(fs);
    }
    cout << "------#" << endl;
    if(lp <= 1) sub_main(cin);
#else
    sub_main(cin);
#endif
    return 0;
}


Measured memory_bytes: 307672