Problem:
Score : 1000 points

Problem Statement

Snuke has come up with the following problem.

You are given a sequence d of length N.
Find the number of the undirected graphs with N vertices labeled 1,2,...,N satisfying the following conditions, modulo 10^{9} + 7:

The graph is simple and connected.

The degree of Vertex i is d_i.

When 2 \leq N, 1 \leq d_i \leq N-1, {\rm Σ} d_i = 2(N-1), it can be proved that the answer to the problem is \frac{(N-2)!}{(d_{1} -1)!(d_{2} - 1)! ... (d_{N}-1)!}.

Snuke is wondering what the answer is when 3 \leq N, 1 \leq d_i \leq N-1, { \rm Σ} d_i = 2N.
Solve the problem under this condition for him.

Constraints

3 \leq N \leq 300

1 \leq d_i \leq N-1

{ \rm Σ} d_i = 2N

Partial Scores

In the test set worth 200 points, N \leq 5.

In the test set worth another 200 points, N \leq 18.

In the test set worth another 300 points, N \leq 50.

Input

Input is given from Standard Input in the following format:

N
d_1 d_2 ... d_{N}

Output

Print the answer.

Sample Input 1

5
1 2 2 3 2

Sample Output 1

6

There are six graphs as shown below:

Sample Input 2

16
2 1 3 1 2 1 4 1 1 2 1 1 3 2 4 3

Sample Output 2

555275958

Be sure to find the answer modulo 10^{9} + 7.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.Reader;
import java.io.InputStreamReader;
import java.io.InputStream;

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

    static class TaskB {
        public void solve(int testNumber, MyInput in, PrintWriter out) {
            int n = in.nextInt();
            int[] d = in.nextIntArray(n);

            if (n <= 5) {
                int m = n * (n - 1) / 2;
                int[][] es = new int[m][];
                for (int i = 0, k = 0; i < n; i++) {
                    for (int j = i + 1; j < n; j++) {
                        es[k++] = new int[]{i, j};
                    }
                }

                long ans = 0;
                UnionFind2 uf = new UnionFind2(n);
                LOOP:
                for (int i = 0; i < 1 << m; i++) {
                    uf.clear();
                    for (int j = 0; j < m; j++) {
                        if ((i >>> j & 1) == 1) {
                            uf.union(es[j][0], es[j][1]);
                        }
                    }
                    if (uf.size(0) == n) {
                        for (int j = 0; j < n; j++) {
                            if (uf.deg[j] != d[j]) continue LOOP;
                        }
                        ans++;
                    }
                }
                out.println(ans);
            }
        }

    }

    static class MyInput {
        private final BufferedReader in;
        private static int pos;
        private static int readLen;
        private static final char[] buffer = new char[1024 * 8];
        private static char[] str = new char[500 * 8 * 2];
        private static boolean[] isDigit = new boolean[256];
        private static boolean[] isSpace = new boolean[256];
        private static boolean[] isLineSep = new boolean[256];

        static {
            for (int i = 0; i < 10; i++) {
                isDigit['0' + i] = true;
            }
            isDigit['-'] = true;
            isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
            isLineSep['\r'] = isLineSep['\n'] = true;
        }

        public MyInput(InputStream is) {
            in = new BufferedReader(new InputStreamReader(is));
        }

        public int read() {
            if (pos >= readLen) {
                pos = 0;
                try {
                    readLen = in.read(buffer);
                } catch (IOException e) {
                    throw new RuntimeException();
                }
                if (readLen <= 0) {
                    throw new MyInput.EndOfFileRuntimeException();
                }
            }
            return buffer[pos++];
        }

        public int nextInt() {
            int len = 0;
            str[len++] = nextChar();
            len = reads(len, isSpace);
            int i = 0;
            int ret = 0;
            if (str[0] == '-') {
                i = 1;
            }
            for (; i < len; i++) ret = ret * 10 + str[i] - '0';
            if (str[0] == '-') {
                ret = -ret;
            }
            return ret;
        }

        public char nextChar() {
            while (true) {
                final int c = read();
                if (!isSpace[c]) {
                    return (char) c;
                }
            }
        }

        int reads(int len, boolean[] accept) {
            try {
                while (true) {
                    final int c = read();
                    if (accept[c]) {
                        break;
                    }
                    if (str.length == len) {
                        char[] rep = new char[str.length * 3 / 2];
                        System.arraycopy(str, 0, rep, 0, str.length);
                        str = rep;
                    }
                    str[len++] = (char) c;
                }
            } catch (MyInput.EndOfFileRuntimeException e) {
            }
            return len;
        }

        public int[] nextIntArray(final int n) {
            final int[] res = new int[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextInt();
            }
            return res;
        }

        static class EndOfFileRuntimeException extends RuntimeException {
        }

    }

    static class UnionFind2 {
        private int[] data;
        public int[] deg;

        public UnionFind2(int size) {
            data = new int[size];
            deg = new int[size];
            clear();
        }

        public void clear() {
            Arrays.fill(data, -1);
            Arrays.fill(deg, 0);
        }

        public int root(int x) {
            return data[x] < 0 ? x : (data[x] = root(data[x]));
        }

        public void union(int x, int y) {
            deg[x]++;
            deg[y]++;
            if ((x = root(x)) != (y = root(y))) {
                if (data[y] < data[x]) {
                    final int t = x;
                    x = y;
                    y = t;
                }
                data[x] += data[y];
                data[y] = x;
            }
        }

        public int size(int x) {
            return -data[root(x)];
        }

    }
}