You are given an integer *m* as a product of integers *a*<sub class="lower-index">1</sub>, *a*<sub class="lower-index">2</sub>, ... *a*<sub class="lower-index">*n*</sub> <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/cf060eec22f7a6ddd13992efe2ebf6d08fde945a.png" style="max-width: 100.0%;max-height: 100.0%;"/>. 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 (10<sup class="upper-index">9</sup> + 7).
The first line contains positive integer *n* (1 ≤ *n* ≤ 500). The second line contains space-separated integers *a*<sub class="lower-index">1</sub>, *a*<sub class="lower-index">2</sub>, ..., *a*<sub class="lower-index">*n*</sub> (1 ≤ *a*<sub class="lower-index">*i*</sub> ≤ 10<sup class="upper-index">9</sup>).
ans=[0 for x in range(100001)]
#######find prime factors
# Python3 program to print prime factors
# and their powers.
import math

# Function to calculate all the prime
# factors and count of every prime factor
def factorize(n):
    count = 0;

    # count the number of
    # times 2 divides
    while ((n % 2 > 0) == False):

        # equivalent to n = n / 2;
        n >>= 1;
        count += 1;

    # if 2 divides it
    if (count > 0):
        ans[2]+=count

    # check for all the possible
    # numbers that can divide it
    for i in range(3, int(math.sqrt(n)) + 1):
        count = 0;
        while (n % i == 0):
            count += 1;
            n = int(n / i);
        if (count > 0):
            ans[i]+=count;
        i += 2;

    # if n at the end is a prime number.
    if (n > 2):
        ans[n]+=1
mod=10**9+7

def fact(n):
    f=[1 for x in range(n+1)]
    for i in range(1,n+1):
        f[i]=(f[i-1]*i)%mod
    return f

f=fact(200000)
def ncr(n,r):
    result=(f[n]*pow(f[r],mod-2,mod)*pow(f[n-r],mod-2,mod))%mod
    return result

n=int(input())
arr=[int(x) for x in input().split()]
for item in arr:
    factorize(item)
result=1
for i in range(1,100001):
    if ans[i]>0:
        result=result*ncr(ans[i]+n-1,n-1)
        result=result%mod
print(result)