Problem: There are N dishes, numbered 1, 2, \ldots, N. Initially, for each i (1 \leq i \leq N), Dish i has a_i (1 \leq a_i \leq 3) pieces of sushi on it.

Taro will perform the following operation repeatedly until all the pieces of sushi are eaten:

* Roll a die that shows the numbers 1, 2, \ldots, N with equal probabilities, and let i be the outcome. If there are some pieces of sushi on Dish i, eat one of them; if there is none, do nothing.



Find the expected number of times the operation is performed before all the pieces of sushi are eaten.

Constraints

* All values in input are integers.
* 1 \leq N \leq 300
* 1 \leq a_i \leq 3

Input

Input is given from Standard Input in the following format:


N
a_1 a_2 \ldots a_N


Output

Print the expected number of times the operation is performed before all the pieces of sushi are eaten. The output is considered correct when the relative difference is not greater than 10^{-9}.

Examples

Input

3
1 1 1


Output

5.5


Input

1
3


Output

3


Input

2
1 2


Output

4.5


Input

10
1 3 2 3 3 2 3 2 1 3


Output

54.48064457488221

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.math.*;

 
 public class Main{
   static class Pair implements Comparable<Pair>{
   int a;
   int b;
   public Pair(int x,int y){a=x;b=y;}
   public Pair(){}
   public int compareTo(Pair p1){
       if(a == p1.a)
       return b - p1.b;
       return a - p1.a;
   }
 }
static class TrieNode{
  TrieNode[]child;
  int w;
  boolean term;
  TrieNode(){
    child = new TrieNode[26];  
  }
}
  public static int gcd(int a,int b)
  {
    if(a<b)
      return gcd(b,a);
    if(b==0)
      return a;
    return gcd(b,a%b);
    
  }
  //static long ans = 0;
  static long mod = (long)(1e9+7);
   
    public static void main(String[] args) throws Exception {
       new Thread(null, null, "Anshum Gupta", 99999999) {
            public void run() {
                try {
                    solve();
                } catch(Exception e) {
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }.start();
    }
///static long[][]dp;
static int maxV;
static long pow(long x,long y){
    if(y == 0)return 1;
    if(y==1)return x;
    long a = pow(x,y/2);
    a = (a*a)%mod;
    if(y%2==0){
        return a;
    }
    return (a*x)%mod;
}
static int n;
static double find(int c1,int c2,int c3){
    if(c1==0 && c2==0 && c3==0)return 0;
    if(c2==0 && c3==0 && c1==1)return n;
    double ans = 0;
    if(dp[c1][c2][c3]!=-1)return dp[c1][c2][c3];
    if(c3 > 0){
        ans += find(c1,c2+1,c3-1)*c3/(c1+c2+c3);
    }
    if(c2 > 0){
     ans += find(c1+1,c2-1,c3)*c2/(c1+c2+c3);   
    }
    if(c1 > 0){
        ans += find(c1-1,c2,c3)*c1/(c1+c2+c3);
    }
    ans += n*1.0/(c1+c2+c3);
    return dp[c1][c2][c3] = ans;
    
}
static double[][][]dp;
static void dfs
(ArrayList<ArrayList<Integer>>adj,int sv,boolean[]vis,int[]x){}
static TrieNode root;
 public static void solve() throws Exception {
   // solve the problem here
   MyScanner s = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out), true);
        int t = 1;
        int tc = 0;
      //  maxV = 300000;
        while(tc++<t){
            n = s.nextInt();
            int[]a=new int[n];
            dp = new double[n+1][n+1][n+1];
            for(int i=0;i<=n;i++)
            for(int j=0;j<=n;j++)
            Arrays.fill(dp[i][j],-1);
            int cnt1=0,cnt2=0,cnt3=0;
            int cnt = 0;
            for(int i=0;i<n;i++){
                a[i]=s.nextInt();
                if(a[i]==1)cnt1++;
                else if(a[i]==2)cnt2++;
                else cnt3++;
            }
            out.println(find(cnt1,cnt2,cnt3));
          //  out.println(dp[cnt1][cnt2][cnt3]);
        }
        out.flush();
}
 
     
 
 
 
    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;
 
    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;
 
        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
 
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt() { return Integer.parseInt(next()); }
        long nextLong() { return Long.parseLong(next()); }
        double nextDouble() { return Double.parseDouble(next()); }
         
        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    //--------------------------------------------------------
}