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>).
import itertools

def prime_factors(n):
    g = []
    for i in itertools.chain([2], itertools.count(3, 2)):
        if n <= 1:
            break
        t = 0
        while n % i == 0:
            n //= i
            t+=1
        if t:
          g.append(t)
    return g        
from math import factorial
x = 1
n = int(input())
for i in map(int,input().split()):
  x*=i
f = prime_factors(x)
ans = 1
for i in f:
  ans*=factorial(i+n-1)/(factorial(n-1)*factorial(i))
print(int(ans))