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>).
from collections import defaultdict


n = int(input().strip())

a = map(int,input().strip().split())

def sieve(n):
    list = [False]*(n+1)
    Primes = []
    for i in range(2,n+1):
        if not list[i]:
            Primes.append(i)
            for j in range(2*i,n+1,i):
                list[j]=True
    return Primes

primes = sieve(10**5)
reduced = defaultdict(int)

def prime_factorization(num):
    #global reduced,primes
    #primes = sieve(num) # if primes are not prebuilt
    for prime in primes:
        if prime<=num and num%prime == 0:
            while num%prime == 0:
                reduced[prime] += 1
                num//=prime
    if num != 1:
        reduced[num] +=1

_ = list(map(prime_factorization,a))

pascals = [[1]]
for i in range(2,10**3):
    pascals.append([])
    for j in range(i):
        cur = 0
        if j != 0:
            cur+=pascals[-2][j-1]
        if j+1 != i:
            cur += pascals[-2][j]
        pascals[-1].append(cur)
        
result = 1        
for prime in reduced:
    #print(prime,reduced[prime])
    result*=pascals[reduced[prime]+n-1][n-1]
    result%=1000000007

print(result)
    
