// --------------------------------------------------<TEMPLATE>--------------------------------------------------
// --------------------<optimizations>--------------------
#pragma GCC optimize("O3")
//(UNCOMMENT WHEN HAVING LOTS OF RECURSIONS)\
#pragma comment(linker, "/stack:200000000")
//(UNCOMMENT WHEN TRYING TO BRUTEFORCE WITH A LOT OF LOOPS)\
#pragma GCC optimize("unroll-loops")

// -------------------</optimizations>--------------------

// ---------------<Headers and namespaces>----------------
#include <algorithm>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <ratio>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;

/*
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/rope>
using namespace __gnu_pbds;
using namespace __gnu_cxx;

// ---------------</Headers and namespaces>---------------

// -----------------<Defines and typedefs>----------------
typedef tree<int,null_type,less<int>,rb_tree_tag,
tree_order_statistics_node_update> indexed_set;
// order_of_key (val): returns the no. of values less than val
// find_by_order (k): returns the iterator to kth largest element.(0-based)
*/

typedef long long ll;
typedef long double LD;
#define int ll
#define double LD
#define pb push_back
#define mp make_pair
#define REP(i,n) for (int i = 0; i < n; i++)
#define FOR(i,a,b) for (int i = a; i < b; i++)
#define REPD(i,n) for (int i = n-1; i >= 0; i--)
#define FORD(i,a,b) for (int i = a; i >= b; i--)
#define remax(a,b) a = max(a,b)
#define remin(a,b) a = min(a,b)
#define all(v) v.begin(),v.end()
typedef map<int,int> mii;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef pair<int,int> pii;
typedef vector<pii> vpii;
#define F first
#define S second
#define PQ(type) priority_queue<type>
#define PQD(type) priority_queue<type,vector<type>,greater<type> >
#define ITR :: iterator it
#define WL(t) while(t --)
#define SZ(x) ((int)(x).size())
#define runtime() ((double)clock() / CLOCKS_PER_SEC)
#define TR(container,it) for(typeof(container.begin()) it=container.begin();it!=container.end();it++)
#define sqr(x) ((x)*(x))

// -----<SCANF>-----
#define sfi(x) scanf("%d",&x);
#define sfi2(x,y) scanf("d",&x,&y);
#define sfi3(x,y,z) scanf("d%d",&x,&y,&z);

#define sfl(x) scanf("%lld",&x);
#define sfl2(x,y) scanf("lld",&x,&y);
#define sfl3(x,y,z) scanf("lld%lld",&x,&y,&z);

#define sfs(x) scanf("%s",&x);
#define sfs2(x,y) scanf("s",&x,&y);
#define sfs3(x,y,z) scanf("s%s",&x,&y,&z);
// ----</SCANF>-----

// ----<PRINTF>-----
#define pfi(x) printf("%d\n",x);
#define pfi2(x,y) printf("%d %d\n",x,y);
#define pfi3(x,y,z) printf("%d %d %d\n",x,y,z);

#define pfl(x) printf("%lld\n",x);
#define pfl2(x,y) printf("%lld %lld\n",x,y);
#define pfl3(x,y,z) printf("%lld %lld %lld\n",x,y,z);

#define pfs(x) printf("%s\n",x);
#define pfs2(x,y) printf("%s %s\n",x,y);
#define pfs3(x,y,z) printf("%s %s %s\n",x,y,z);
// ----</PRINTF>----

#define FLSH fflush(stdout)
#define fileIO(name) \
    freopen(name".in", "r", stdin); \
    freopen(name".out", "w", stdout);
#define PRECISION(x) cout << fixed << setprecision(x);
#define FAST_IO ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);

// ----------------</Defines and typedefs>----------------

// -------------------<Debugging stuff>-------------------
#define TRACE

#ifdef TRACE
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
	cerr << name << " : " << arg1 << std::endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
	const char* comma = strchr(names + 1, ',');cerr.write(names, comma - names) << " : " << arg1<<" | ";__f(comma+1, args...);
}
#else
#define trace(...)
#endif

// ------------------</Debugging stuff>-------------------

// ------------------------<Consts>-----------------------
const int MAXN = 1000005;
const int SQRTN = 1003;
const int LOGN = 22;
const double PI=acos(-1);
const int INF = 1000000000;
const int MOD = 1000000007;
const int FMOD = 998244353;
const double eps = 1e-9;

// -----------------------</Consts>-----------------------

// -------------------------<RNG>-------------------------
mt19937 RNG(chrono::steady_clock::now().time_since_epoch().count());
#define SHUF(v) shuffle(all(v), RNG);
// Use mt19937_64 for 64 bit random numbers.

// ------------------------</RNG>-------------------------

// -----------------<Modular Arithmetic>------------------
template<typename T> T gcd(T a, T b){return(b?__gcd(a,b):a);}
template<typename T> T lcm(T a, T b){return(a*(b/gcd(a,b)));}
int add(int a, int b, int c){int res=a+b;return(res>=c?res-c:res);}
int mod_neg(int a, int b, int c){int res;if(abs(a-b)<c)res=a-b;else res=(a-b)%c;return(res<0?res+c:res);}
int mul(int a, int b, int c){ll res=(ll)a*b;return(res>=c?res%c:res);}
ll mulmod(ll a,ll b, ll m){ll q = (ll)(((LD)a*(LD)b)/(LD)m);ll r=a*b-q*m;if(r>m)r%=m;if(r<0)r+=m;return r;}
template<typename T>T expo(T e, T n){T x=1,p=e;while(n){if(n&1)x=x*p;p=p*p;n>>=1;}return x;}
template<typename T>T power(T e, T n, T m){T x=1,p=e;while(n){if(n&1)x=mul(x,p,m);p=mul(p,p,m);n>>=1;}return x;}
template<typename T>T extended_euclid(T a, T b, T &x, T &y){T xx=0,yy=1;y=0;x=1;while(b){T q=a/b,t=b;b=a%b;a=t;\
t=xx;xx=x-q*xx;x=t;t=yy;yy=y-q*yy;y=t;}return a;}
template<typename T>T mod_inverse(T a, T n){T x,y,z=0;T d=extended_euclid(a,n,x,y);return(d>1?-1:mod_neg(x,z,n));}
template <typename T> int sgn(T val) {
    return (T(0) < val) - (val < T(0));
}

// -----------------</Modular Arithmetic>-----------------
// --------------------------------------------------</TEMPLATE>--------------------------------------------------
#define m 305
double dp[m][m][m];

signed main(){
	FAST_IO
	PRECISION(10)
	int n;
	cin>>n;
	double nd = n;
	int a[n];
	int cnt[4] = {0};
	for(int i = 0; i<n; i++){
        cin>>a[i];
        cnt[a[i]]++;
	}
	//find expected number of rolls such that i comes up at least a[i] times and at least one of the freq is a[i] and i is seen in the end
	for(int i = 0; i<=n; i++){
        for(int j = 0; j<=n; j++){
            for(int k = 0; k<=n; k++){
                dp[i][j][k] = 0;
            }
        }
	}
	for(int i = 1; i<=n; i++){
        double id = i;
        dp[i][0][0] = nd / i + dp[i-1][0][0];
	}
	for(int i = 1; i<=n; i++){
        for(int j = 0; j<=n-i; j++){
            if(j==0){
                double id = i;
                dp[j][i][0] = nd/id+ dp[1][i-1][0];
            }
            else{
                double id = i;
                double jd = j;
                dp[j][i][0] = nd/(jd+id) + jd/(jd+id) * dp[j-1][i][0] + id/(id+jd) * dp[j+1][i-1][0];
            }
        }
	}
	for(int i = 1; i<=n; i++){
        double id = i;
        for(int j = 0; j<=n-i; j++){
            double jd = j;
            if(j==0)
            for(int k = 0; k<=n-i-j; k++){
                double kd = k;
                if(k==0){
                    dp[0][0][i] = nd/id + dp[0][1][i-1];
                }
                else{
                    dp[k][0][i] = nd/(id+kd) + kd/(kd+id)*dp[k-1][0][i] + id/(kd+id)*dp[k][1][i-1];
                }
            }
            else{
                for(int k = 0; k<= n-i-j; k++){
                    double kd = k;
                    if(k==0){
                        dp[0][j][i] = nd/(id+jd) + jd/(jd+id) * dp[1][j-1][i] + id/(id+jd) * dp[0][j+1][i-1];

                    }
                    else{
                        dp[k][j][i] = nd/(id+jd+kd) + kd/(id+jd+kd)*dp[k-1][j][i] + jd/(id+jd+kd)*dp[k+1][j-1][i] + id/(id+jd+kd)*dp[k][j+1][i-1];

                    }
                }
            }
        }
	}
	cout<<dp[cnt[1]][cnt[2]][cnt[3]];
	return 0;
}


Measured memory_bytes: 438528