n = int(input())

m = {}
def decomposition(x):
    i = 2
    while i <= x/i:
        while x % i == 0:
            x = int(x/i)
            if i not in m:
                m[i] = 1
            else:
                m[i] += 1
        i += 1
    if x > 1:
        if x not in m:
            m[x] = 1
        else:
            m[x] += 1

r = 1
while n:
    k = int(input())
    decomposition(k)
    n -= 1
for v in m:
    r = r * (m[v] + 1)
mod = 1e9 + 7
print(int(r % mod))