You are given an integer m as a product of integers a1, a2, ... an <image>. Your task is to find the number of distinct decompositions of number m into the product of n ordered positive integers.

Decomposition into n products, given in the input, must also be considered in the answer. As the answer can be very large, print it modulo 1000000007 (109 + 7).

Input

The first line contains positive integer n (1 ≤ n ≤ 500). The second line contains space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 109).

Output

In a single line print a single number k — the number of distinct decompositions of number m into n ordered multipliers modulo 1000000007 (109 + 7).

Examples

Input

1
15


Output

1


Input

3
1 1 2


Output

3


Input

2
5 7


Output

4

Note

In the second sample, the get a decomposition of number 2, you need any one number out of three to equal 2, and the rest to equal 1.

In the third sample, the possible ways of decomposing into ordered multipliers are [7,5], [5,7], [1,35], [35,1].

A decomposition of positive integer m into n ordered multipliers is a cortege of positive integers b = {b1, b2, ... bn} such that <image>. Two decompositions b and c are considered different, if there exists index i such that bi ≠ ci.
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.Map;

/**
 * Created by dhamada on 15/05/21.
 */
public class A {
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);

        prec(100000);

        int[] p = generatePrimes(32000);
        int n = in.nextInt();
        Map<Integer,Integer> m = new HashMap<>();
        for (int i = 0 ; i < n ; i++) {
            int x = in.nextInt();
            for (int pi : p) {
                if (x < pi) {
                    break;
                }
                int ct = 0;
                while (x % pi == 0) {
                    ct++;
                    x /= pi;
                }
                if (!m.containsKey(pi)) {
                    m.put(pi, ct);
                } else {
                    m.put(pi, m.get(pi)+ct);
                }
            }
            if (x >= 2) {
                if (!m.containsKey(x)) {
                    m.put(x, 1);
                } else {
                    m.put(x,  m.get(x)+1);
                }
            }
        }

        long ptn = 1;
        for (int v : m.values()) {
            ptn *= comb(v + n - 1, n - 1);
            ptn %= MOD;
        }
        out.println(ptn);
        out.flush();
    }

    static final int MOD = 1000000007;

    static long[] _fact;
    static long[] _invfact;
    static long comb(long ln, long lr) {
        int n = (int)ln;
        int r = (int)lr;
        if (n < 0 || r < 0 || r > n) {
            return 0;
        }
        if (r > n / 2) {
            r = n - r;
        }
        return (((_fact[n] * _invfact[n - r]) % MOD) * _invfact[r]) % MOD;
    }

    static void prec(int n) {
        _fact = new long[n + 1];
        _invfact = new long[n + 1];
        _fact[0] = 1;
        _invfact[0] = 1;
        for (int i = 1; i <= n; i++) {
            _fact[i] = _fact[i - 1] * i % MOD;
            _invfact[i] = inv(_fact[i]);
        }
    }

    static long inv(long a) {
        return pow(a, MOD - 2) % MOD;
    }

    static long pow(long a, long x) {
        long res = 1;
        while (x > 0) {
            if (x % 2 != 0) {
                res = (res * a) % MOD;
            }
            a = (a * a) % MOD;
            x /= 2;
        }
        return res;
    }

    static int[] generatePrimes(int upto) {
        boolean[] isp = new boolean[upto];
        Arrays.fill(isp, true);

        int pi = 0;
        for (int i = 2; i < upto ; i++) {
            if (isp[i]) {
                pi++;
                for (int j = i * 2; j < upto; j += i) {
                    isp[j] = false;
                }
            }
        }

        int[] ret = new int[pi];
        int ri = 0;
        for (int i = 2 ; i < upto ; i++) {
            if (isp[i]) {
                ret[ri++] = i;
            }
        }
        return ret;
    }


    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

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

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

        public char nextChar() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            if ('a' <= c && c <= 'z') {
                return (char)c;
            }
            if ('A' <= c && c <= 'Z') {
                return (char)c;
            }
            throw new InputMismatchException();
        }

        public String nextToken() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char)c);
                c = next();
            } while (!isSpaceChar(c));
            return res.toString();
        }

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

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

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

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

    static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }
}
