You are given a positive integer primeFactors. You are asked to construct a positive integer n that satisfies the following conditions:

• The total count of prime factors of n (with multiplicity) is at most primeFactors.

• The count of nice divisors of n is maximized.

A divisor of n is considered nice if it is divisible by every distinct prime factor of n.

Return the maximum number of nice divisors of n. Since the answer may be very large, return it modulo $10^9 + 7$.

Constraints:

• $1 \le$ primeFactors $\le 10^9$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.