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>).
def SieveOfEratosthenes(n):
    prime = [True for i in range(n + 1)]
    p = 2
    while (p * p <= n):

        if (prime[p] == True):

            for i in range(p * p, n + 1, p):
                prime[i] = False
        p += 1

    l = []
    for p in range(2, n):
        if prime[p]:
            l.append(p)
    return l


def ncr(n, r, p):
    num = den = 1
    for i in range(r):
        num = (num * (n - i)) % p
        den = (den * (i + 1)) % p
    return (num * pow(den,
            p - 2, p)) % p

MOD = 10**9+7
primes = SieveOfEratosthenes(10**5)
n = int(input())
l = [int(zax) for zax in input().split()]


map = {}
for x in l:
    check = True
    for p in primes:
        if x%p==0:
            check = False
            while x%p==0:
                if p in map:
                    map[p]+=1
                else:
                    map[p]=1
                x//=p
    if check:
        if x!=1:
            if x in map:
                map[x]+=1
            else:
                map[x]=1

count = 1
for x in map:
    count*=ncr(n-1+map[x],n-1,MOD)
    count%=MOD
print(count)