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:
/*input
2
1 2
*/
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.PriorityQueue;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author masterbios
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        CLinovaAndKingdom solver = new CLinovaAndKingdom();
        solver.solve(1, in, out);
        out.close();
    }

    static class CLinovaAndKingdom {

        final int MAXN = (int) (3e2) + 10;
        final long MOD = (long) (1e9) + 7;
        int group[] = new int[4];
        double dp[][][] = new double[MAXN][MAXN][MAXN];
        int n;

        public void solve(int testNumber, InputReader in, PrintWriter out) {

            this.n = in.nextInt();
            for (int i = 0, x = 0; i < n; i++) {
                x = in.nextInt();
                group[x]++;
            }
            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] = -1.0d;
                }
            }
            double ans = solve(group[1], group[2], group[3]);
            out.printf("%.14f\n", ans);

        }

        public double solve(int one, int two, int three) {

            if (one + two + three == 0) return 0.0d;

            if (dp[one][two][three] != -1.0d) return dp[one][two][three];

            double ans = 0.0d, sum = one + two + three;

            if (one > 0) {
                double cc = (one * 1.0d) / sum;
                cc *= solve(one - 1, two, three);
                ans += cc;
            }

            if (two > 0) {
                double cc = (two * 1.0d) / sum;
                cc *= solve(one + 1, two - 1, three);
                ans += cc;
            }

            if (three > 0) {
                double cc = (three * 1.0d) / sum;
                cc *= solve(one, two + 1, three - 1);
                ans += cc;
            }
        
            ans += this.n / sum;

            return dp[one][two][three] = ans;
        }

        public int max(int ...a) {
            int max = Integer.MIN_VALUE;
            for (int i : a) max = Math.max(max, i);
            return max;
        }

        public int min(int ...a) {
            int min = Integer.MAX_VALUE;
            for (int i : a) min = Math.min(min, i);
            return min;
        }

        public long max(long ...a) {
            long max = Long.MIN_VALUE;
            for (long i : a) max = Math.max(max, i);
            return max;
        }

        public long min(long ...a) {
            long min = Long.MAX_VALUE;
            for (long i : a) min = Math.min(min, i);
            return min;
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreElements()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

    }
}