import collections
MOD = 10**9+7

def helper(n):
    i = 2
    while i*i <= n:
        while n%i==0:
            d[i] += 1
            n /= i
        i += 1
    if n != 1:
        d[n] +=1

d = collections.defaultdict(int)
n = int(input())
for _ in range(n):
    m = int(input())
    helper(m)
ans = 1
for k in d:
    ans = ans * (d[k]+1)%MOD
print(ans)