Kyoya Ootori has a bag with n colored balls that are colored with k different colors. The colors are labeled from 1 to k. Balls of the same color are indistinguishable. He draws balls from the bag one by one until the bag is empty. He noticed that he drew the last ball of color i before drawing the last ball of color i + 1 for all i from 1 to k - 1. Now he wonders how many different ways this can happen. 

Input

The first line of input will have one integer k (1 ≤ k ≤ 1000) the number of colors.

Then, k lines will follow. The i-th line will contain ci, the number of balls of the i-th color (1 ≤ ci ≤ 1000).

The total number of balls doesn't exceed 1000.

Output

A single integer, the number of ways that Kyoya can draw the balls from the bag as described in the statement, modulo 1 000 000 007. 

Examples

Input

3
2
2
1


Output

3


Input

4
1
2
3
4


Output

1680

Note

In the first sample, we have 2 balls of color 1, 2 balls of color 2, and 1 ball of color 3. The three ways for Kyoya are: 
    
    
      
    1 2 1 2 3  
    1 1 2 2 3  
    2 1 1 2 3  
    
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

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

    static class TaskA {
        static int[][] fif = NT.enumFIF(20000, NT.MOD7I);

        public void solve(int testNumber, FastReader in, PrintWriter out) {
            int k = in.nextInt();
            int[] c = in.nextIntArray(k);
            int tot = 0;
            long ret = 1L;
            for (int i = 0; i < k; ++i) {
                ret = ret * NT.C(tot + c[i] - 1, c[i] - 1, NT.MOD7I, fif) % NT.MOD7I;
                tot += c[i];
            }
            out.println(ret);
        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar;
        private int pnumChars;
        private FastReader.SpaceCharFilter filter;

        public FastReader(InputStream stream) {
            this.stream = stream;
        }

        private int pread() {
            if (pnumChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= pnumChars) {
                curChar = 0;
                try {
                    pnumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (pnumChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = pread();
            while (isSpaceChar(c))
                c = pread();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = pread();
            }
            int res = 0;
            do {
                if (c == ',') {
                    c = pread();
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = pread();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

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

        private boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        private static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class NT {
        public static final int MOD7I = (int) 1e9 + 7;

        public static long C(int n, int r, int mod, int[][] fif) {
            if (n < 0 || r < 0 || r > n) return 0;
            return (long) fif[0][n] % mod * fif[1][r] % mod * fif[1][n - r] % mod;
        }

        public static int[][] enumFIF(int n, int mod) {
            int[] f = new int[n + 1];
            int[] invf = new int[n + 1];
            f[0] = 1;
            for (int i = 1; i <= n; i++) {
                f[i] = (int) ((long) f[i - 1] * i % mod);
            }
            long a = f[n];
            long b = mod;
            long p = 1, q = 0;
            while (b > 0) {
                long c = a / b;
                long d;
                d = a;
                a = b;
                b = d % b;
                d = p;
                p = q;
                q = d - c * q;
            }
            invf[n] = (int) (p < 0 ? p + mod : p);
            for (int i = n - 1; i >= 0; i--) {
                invf[i] = (int) ((long) invf[i + 1] * (i + 1) % mod);
            }
            return new int[][]{f, invf};
        }

    }
}

