Language: Java

import java.io.*;
import java.util.*;

public class s409580149 {
    static int n, a[];
    static double dp[][][];

    static void solve() {
        n = ni();
        a = na(n);
        dp = new double[n + 1][n + 1][n + 1];
        for (int i = 0; i < n + 1; i++) fill(dp[i], -1);
        dp[0][0][0] = 0;
        int cnt[] = new int[3];
        for (int i = 0; i < n; i++) {
            cnt[a[i] - 1]++;
        }
        double ans = rec(cnt[0], cnt[1], cnt[2]);
        out.println(ans);
    }

    static double rec(int i, int j, int k) {
        if (dp[i][j][k] != -1) return dp[i][j][k];
        double ret = 0;
        double p = ((double) i + j + k) / n;
        double pi = (double) i / n;
        double pj = (double) j / n;
        double pk = (double) k / n;
        ret += 1 / p;
        if (i > 0) ret += pi / p * rec(i - 1, j, k);
        if (j > 0) ret += pj / p * rec(i + 1, j - 1, k);
        if (k > 0) ret += pk / p * rec(i, j + 1, k - 1);
        return dp[i][j][k] = ret;
    }

    static final long mod = (long) 1e9 + 7;
    static final int dx[] = {-1, 0, 1, 0}, dy[] = {0, -1, 0, 1};
    static final int[] dx8 = {-1, -1, -1, 0, 0, 1, 1, 1}, dy8 = {-1, 0, 1, -1, 1, -1, 0, 1};
    static final int inf = Integer.MAX_VALUE / 2;
    static final long linf = Long.MAX_VALUE / 3;
    static final double dinf = Double.MAX_VALUE / 3;
    static final double eps = 1e-10;
    static final double pi = Math.PI;
    static StringBuilder sb = new StringBuilder();
    static InputStream is;
    static PrintWriter out;
    static String INPUT = "";

    static void reverse(int ar[]) {
        int len = ar.length;
        for (int i = 0; i < len / 2; i++) {
            int t = ar[i];
            ar[i] = ar[len - 1 - i];
            ar[len - 1 - i] = t;
        }
    }

    static void reverse(long ar[]) {
        int len = ar.length;
        for (int i = 0; i < len / 2; i++) {
            long t = ar[i];
            ar[i] = ar[len - 1 - i];
            ar[len - 1 - i] = t;
        }
    }

    static void reverse(double ar[]) {
        int len = ar.length;
        for (int i = 0; i < len / 2; i++) {
            double t = ar[i];
            ar[i] = ar[len - 1 - i];
            ar[len - 1 - i] = t;
        }
    }

    static void reverse(char ar[]) {
        int len = ar.length;
        for (int i = 0; i < len / 2; i++) {
            char t = ar[i];
            ar[i] = ar[len - 1 - i];
            ar[len - 1 - i] = t;
        }
    }

    static String getReverse(String s) {
        char c[] = s.toCharArray();
        reverse(c);
        s = String.valueOf(c);
        return s;
    }

    static <T> void reverse(List<T> ls) {
        int sz = ls.size();
        for (int i = 0; i < sz / 2; i++) {
            T t = ls.get(i);
            ls.set(i, ls.get(sz - 1 - i));
            ls.set(sz - 1 - i, t);
        }
    }

    static <T> void reverse(T[] ar) {
        int len = ar.length;
        for (int i = 0; i < len / 2; i++) {
            T t = ar[i];
            ar[i] = ar[len - 1 - i];
            ar[len - 1 - i] = t;
        }
    }

    static void sbnl() {
        sb.append("\n");
    }

    static int lowerBound(int[] a, int x) {
        int l = -1, r = a.length;
        while (r - l > 1) {
            int c = (l + r) / 2;
            if (a[c] < x) {
                l = c;
            } else {
                r = c;
            }
        }
        return r;
    }

    static int upperBound(int[] a, int x) {
        int l = -1, r = a.length;
        while (r - l > 1) {
            int c = (l + r) / 2;
            if (a[c] <= x) {
                l = c;
            } else {
                r = c;
            }
        }
        return r;
    }

    static int rlowerBound(int[] a, int x) {
        int l = -1, r = a.length;
        while (r - l > 1) {
            int c = (l + r) / 2;
            if (a[c] > x) {
                l = c;
            } else {
                r = c;
            }
        }
        return r;
    }

    static int rupperBound(int[] a, int x) {
        int l = -1, r = a.length;
        while (r - l > 1) {
            int c = (l + r) / 2;
            if (a[c] >= x) {
                l = c;
            } else {
                r = c;
            }
        }
        return r;
    }

    static int lowerBound(long[] a, long x) {
        int l = -1, r = a.length;
        while (r - l > 1) {
            int c = (l + r) / 2;
            if (a[c] < x) {
                l = c;
            } else {
                r = c;
            }
        }
        return r;
    }

    static int upperBound(long[] a, long x) {
        int l = -1, r = a.length;
        while (r - l > 1) {
            int c = (l + r) / 2;
            if (a[c] <= x) {
                l = c;
            } else {
                r = c;
            }
        }
        return r;
    }

    static int rlowerBound(long[] a, long x) {
        int l = -1, r = a.length;
        while (r - l > 1) {
            int c = (l + r) / 2;
            if (a[c] > x) {
                l = c;
            } else {
                r = c;
            }
        }
        return r;
    }

    static int rupperBound(long[] a, long x) {
        int l = -1, r = a.length;
        while (r - l > 1) {
            int c = (l + r) / 2;
            if (a[c] >= x) {
                l = c;
            } else {
                r = c;
            }
        }
        return r;
    }

    static int lowerBound(double[] a, double x) {
        int l = -1, r = a.length;
        while (r - l > 1) {
            int c = (l + r) / 2;
            if (a[c] < x) {
                l = c;
            } else {
                r = c;
            }
        }
        return r;
    }

    static int upperBound(double[] a, double x) {
        int l = -1, r = a.length;
        while (r - l > 1) {
            int c = (l + r) / 2;
            if (a[c] <= x) {
                l = c;
            } else {
                r = c;
            }
        }
        return r;
    }

    static int rlowerBound(double[] a, double x) {
        int l = -1, r = a.length;
        while (r - l > 1) {
            int c = (l + r) / 2;
            if (a[c] > x) {
                l = c;
            } else {
                r = c;
            }
        }
        return r;
    }

    static int rupperBound(double[] a, double x) {
        int l = -1, r = a.length;
        while (r - l > 1) {
            int c = (l + r) / 2;
            if (a[c] >= x) {
                l = c;
            } else {
                r = c;
            }
        }
        return r;
    }

    static int lowerBound(char[] a, char x) {
        int l = -1, r = a.length;
        while (r - l > 1) {
            int c = (l + r) / 2;
            if (a[c] < x) {
                l = c;
            } else {
                r = c;
            }
        }
        return r;
    }

    static int upperBound(char[] a, char x) {
        int l = -1, r = a.length;
        while (r - l > 1) {
            int c = (l + r) / 2;
            if (a[c] <= x) {
                l = c;
            } else {
                r = c;
            }
        }
        return r;
    }

    static int rlowerBound(char[] a, char x) {
        int l = -1, r = a.length;
        while (r - l > 1) {
            int c = (l + r) / 2;
            if (a[c] > x) {
                l = c;
            } else {
                r = c;
            }
        }
        return r;
    }

    static int rupperBound(char[] a, char x) {
        int l = -1, r = a.length;
        while (r - l > 1) {
            int c = (l + r) / 2;
            if (a[c] >= x) {
                l = c;
            } else {
                r = c;
            }
        }
        return r;
    }

    static <T> int lowerBound(List<T> ls, T x) throws RuntimeException {
        if (ls.size() == 0) return -1;
        if (ls.get(0) instanceof Integer) {
            return ~Collections.binarySearch(
                    ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) >= 0 ? 1 : -1);
        } else if (ls.get(0) instanceof Long) {
            return ~Collections.binarySearch(
                    ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) >= 0 ? 1 : -1);
        } else if (ls.get(0) instanceof Double) {
            return ~Collections.binarySearch(
                    ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) >= 0 ? 1 : -1);
        } else {
            System.err.println(
                    String.format(
                            "%s:数値でないリストを二分探索しています。",
                            Thread.currentThread().getStackTrace()[1].getMethodName()));
            throw new RuntimeException();
        }
    }

    static <T> int upperBound(List<T> ls, T x) throws RuntimeException {
        if (ls.size() == 0) return -1;
        if (ls.get(0) instanceof Integer) {
            return ~Collections.binarySearch(
                    ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) > 0 ? 1 : -1);
        } else if (ls.get(0) instanceof Long) {
            return ~Collections.binarySearch(
                    ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) > 0 ? 1 : -1);
        } else if (ls.get(0) instanceof Double) {
            return ~Collections.binarySearch(
                    ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) > 0 ? 1 : -1);
        } else {
            System.err.println(
                    String.format(
                            "%s:数値でないリストを二分探索しています。",
                            Thread.currentThread().getStackTrace()[1].getMethodName()));
            throw new RuntimeException();
        }
    }

    static <T> int rupperBound(List<T> ls, T x) throws RuntimeException {
        if (ls.size() == 0) return -1;
        if (ls.get(0) instanceof Integer) {
            return ~Collections.binarySearch(
                    ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) < 0 ? 1 : -1);
        } else if (ls.get(0) instanceof Long) {
            return ~Collections.binarySearch(
                    ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) < 0 ? 1 : -1);
        } else if (ls.get(0) instanceof Double) {
            return ~Collections.binarySearch(
                    ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) < 0 ? 1 : -1);
        } else {
            System.err.println(
                    String.format(
                            "%s:数値でないリストを二分探索しています。",
                            Thread.currentThread().getStackTrace()[1].getMethodName()));
            throw new RuntimeException();
        }
    }

    static <T> int rlowerBound(List<T> ls, T x) {
        if (ls.size() == 0) return -1;
        if (ls.get(0) instanceof Integer) {
            return ~Collections.binarySearch(
                    ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) <= 0 ? 1 : -1);
        } else if (ls.get(0) instanceof Long) {
            return ~Collections.binarySearch(
                    ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) <= 0 ? 1 : -1);
        } else if (ls.get(0) instanceof Double) {
            return ~Collections.binarySearch(
                    ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) <= 0 ? 1 : -1);
        } else {
            System.err.println(
                    String.format(
                            "%s:数値でないリストを二分探索しています。",
                            Thread.currentThread().getStackTrace()[1].getMethodName()));
            throw new RuntimeException();
        }
    }

    static int[] concat(int x, int arr[]) {
        int ret[] = new int[arr.length + 1];
        System.arraycopy(arr, 0, ret, 1, ret.length - 1);
        ret[0] = x;
        return ret;
    }

    static int[] concat(int arr[], int x) {
        int ret[] = new int[arr.length + 1];
        System.arraycopy(arr, 0, ret, 0, ret.length - 1);
        ret[ret.length - 1] = x;
        return ret;
    }

    static long[] concat(long x, long arr[]) {
        long ret[] = new long[arr.length + 1];
        System.arraycopy(arr, 0, ret, 1, ret.length - 1);
        ret[0] = x;
        return ret;
    }

    static long[] concat(long arr[], long x) {
        long ret[] = new long[arr.length + 1];
        System.arraycopy(arr, 0, ret, 0, ret.length - 1);
        ret[ret.length - 1] = x;
        return ret;
    }

    static int max(int x, int y) {
        return Math.max(x, y);
    }

    static int min(int x, int y) {
        return Math.min(x, y);
    }

    static int max(int x, int y, int z) {
        x = Math.max(x, y);
        x = Math.max(x, z);
        return x;
    }

    static int min(int x, int y, int z) {
        x = Math.min(x, y);
        x = Math.min(x, z);
        return x;
    }

    static long max(long x, long y) {
        return Math.max(x, y);
    }

    static long min(long x, long y) {
        return Math.min(x, y);
    }

    static long max(long x, long y, long z) {
        x = Math.max(x, y);
        x = Math.max(x, z);
        return x;
    }

    static long min(long x, long y, long z) {
        x = Math.min(x, y);
        x = Math.min(x, z);
        return x;
    }

    static double max(double x, double y) {
        return Math.max(x, y);
    }

    static double min(double x, double y) {
        return Math.min(x, y);
    }

    static double max(double x, double y, double z) {
        x = Math.max(x, y);
        x = Math.max(x, z);
        return x;
    }

    static double min(double x, double y, double z) {
        x = Math.min(x, y);
        x = Math.min(x, z);
        return x;
    }

    static void sort(int[] ar) {
        Arrays.sort(ar);
    }

    static void sort(long[] ar) {
        Arrays.sort(ar);
    }

    static void sort(double[] ar) {
        Arrays.sort(ar);
    }

    static void sort(char[] ar) {
        Arrays.sort(ar);
    }

    static void rsort(int[] ar) {
        Arrays.sort(ar);
        int len = ar.length;
        for (int i = 0; i < len / 2; i++) {
            int tmp = ar[i];
            ar[i] = ar[len - 1 - i];
            ar[len - 1 - i] = tmp;
        }
    }

    static void rsort(long[] ar) {
        Arrays.sort(ar);
        int len = ar.length;
        for (int i = 0; i < len / 2; i++) {
            long tmp = ar[i];
            ar[i] = ar[len - 1 - i];
            ar[len - 1 - i] = tmp;
        }
    }

    static void rsort(double[] ar) {
        Arrays.sort(ar);
        int len = ar.length;
        for (int i = 0; i < len / 2; i++) {
            double tmp = ar[i];
            ar[i] = ar[len - 1 - i];
            ar[len - 1 - i] = tmp;
        }
    }

    static void rsort(char[] ar) {
        Arrays.sort(ar);
        int len = ar.length;
        for (int i = 0; i < len / 2; i++) {
            char tmp = ar[i];
            ar[i] = ar[len - 1 - i];
            ar[len - 1 - i] = tmp;
        }
    }

    static void fill(int arr[], int x) {
        Arrays.fill(arr, x);
    }

    static void fill(long arr[], long x) {
        Arrays.fill(arr, x);
    }

    static void fill(boolean arr[], boolean x) {
        Arrays.fill(arr, x);
    }

    static void fill(double arr[], double x) {
        Arrays.fill(arr, x);
    }

    static void fill(int arr[][], int x) {
        for (int i = 0; i < arr.length; i++) Arrays.fill(arr[i], x);
    }

    static void fill(long arr[][], long x) {
        for (int i = 0; i < arr.length; i++) Arrays.fill(arr[i], x);
    }

    static void fill(double arr[][], double x) {
        for (int i = 0; i < arr.length; i++) Arrays.fill(arr[i], x);
    }

    static void fill(boolean arr[][], boolean x) {
        for (int i = 0; i < arr.length; i++) Arrays.fill(arr[i], x);
    }

    static long plus(long x, long y) {
        long res = (x + y) % mod;
        return res < 0 ? res + mod : res;
    }

    static long sub(long x, long y) {
        long res = (x - y) % mod;
        return res < 0 ? res + mod : res;
    }

    static long mul(long x, long y) {
        long res = (x * y) % mod;
        return res < 0 ? res + mod : res;
    }

    static long div(long x, long y) {
        long res = x * pow(y, mod - 2) % mod;
        return res < 0 ? res + mod : res;
    }

    static long pow(long x, long y) {
        if (y < 0) return 0;
        if (y == 0) return 1;
        if (y % 2 == 1) return (x * pow(x, y - 1)) % mod;
        long root = pow(x, y / 2);
        return root * root % mod;
    }

    public static void main(String[] args) throws Exception {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        solve();
        out.flush();
    }

    private static byte[] inbuf = new byte[1024];
    static int lenbuf = 0, ptrbuf = 0;

    private static int readByte() {
        if (lenbuf == -1) throw new InputMismatchException();
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = is.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0) return -1;
        }
        return inbuf[ptrbuf++];
    }

    private static boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }

    private static int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b))
            ;
        return b;
    }

    @SuppressWarnings("unused")
    private static double nd() {
        return Double.parseDouble(ns());
    }

    @SuppressWarnings("unused")
    private static char nc() {
        return (char) skip();
    }

    private static String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private static char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    @SuppressWarnings("unused")
    private static char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for (int i = 0; i < n; i++) map[i] = ns(m);
        return map;
    }

    @SuppressWarnings("unused")
    private static int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = ni();
        return a;
    }

    @SuppressWarnings("unused")
    private static long[] nla(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) a[i] = nl();
        return a;
    }

    private static int ni() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
            ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    @SuppressWarnings("unused")
    private static long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
            ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
}


Example test case(s):
input: 3
1 1 1

output: 5.5