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Problem J
Product Divisors
Given a sequence of integers $a_1, a_2, \dots a_ n$, compute the number of divisors of their product $A = \prod _{i=1}^ n a_ i$.
Input
The first line contains the number of integers in the sequence $n$ ($1 \le n \le 10^6$).
The second line contains the $n$ space-separated integers $a_1, a_2, \dots , a_ n$ ($1 \le a_ i \le 10^6$).
Output
Output the number of divisors of the product of the input sequence. Since this number may be large, output it modulo $10^9 + 7$.
| Sample Input 1 | Sample Output 1 |
|---|---|
5 1 2 3 4 5 |
16 |
