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>).
n = int(input())
an = input()
if n == 1:
    print('1')
else:
    m = 1
    for i in range(n):
        m = m * int(an.split(' ')[i])
    m_list = list(range(1,m+1))
    mm_list = list(range(1,m+1))
    mmm_list = []
    for i in range(n-1):
        for a in mm_list:
            for b in m_list:
                mmm_list.append(a * b)
        mm_list = mmm_list
        mmm_list = []
    print(int(mm_list.count(m)))