<p>You are given an integer array <code>nums</code>. We call a subset of <code>nums</code> <strong>good</strong> if its product can be represented as a product of one or more <strong>distinct prime</strong> numbers.</p>

<ul>
	<li>For example, if <code>nums = [1, 2, 3, 4]</code>:

	<ul>
		<li><code>[2, 3]</code>, <code>[1, 2, 3]</code>, and <code>[1, 3]</code> are <strong>good</strong> subsets with products <code>6 = 2*3</code>, <code>6 = 2*3</code>, and <code>3 = 3</code> respectively.</li>
		<li><code>[1, 4]</code> and <code>[4]</code> are not <strong>good</strong> subsets with products <code>4 = 2*2</code> and <code>4 = 2*2</code> respectively.</li>
	</ul>
	</li>
</ul>

<p>Return <em>the number of different <strong>good</strong> subsets in </em><code>nums</code><em> <strong>modulo</strong> </em><code>10<sup>9</sup> + 7</code>.</p>

<p>A <strong>subset</strong> of <code>nums</code> is any array that can be obtained by deleting some (possibly none or all) elements from <code>nums</code>. Two subsets are different if and only if the chosen indices to delete are different.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3,4]
<strong>Output:</strong> 6
<strong>Explanation:</strong> The good subsets are:
- [1,2]: product is 2, which is the product of distinct prime 2.
- [1,2,3]: product is 6, which is the product of distinct primes 2 and 3.
- [1,3]: product is 3, which is the product of distinct prime 3.
- [2]: product is 2, which is the product of distinct prime 2.
- [2,3]: product is 6, which is the product of distinct primes 2 and 3.
- [3]: product is 3, which is the product of distinct prime 3.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [4,2,3,15]
<strong>Output:</strong> 5
<strong>Explanation:</strong> The good subsets are:
- [2]: product is 2, which is the product of distinct prime 2.
- [2,3]: product is 6, which is the product of distinct primes 2 and 3.
- [2,15]: product is 30, which is the product of distinct primes 2, 3, and 5.
- [3]: product is 3, which is the product of distinct prime 3.
- [15]: product is 15, which is the product of distinct primes 3 and 5.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 30</code></li>
</ul>

MOD = 10**9 + 7


def get_primes(max_val):
    if max_val <= 1:
        return []

    res = [2]
    for i in range(3, max_val + 1):
        if all(i % p != 0 for p in res):
            res.append(i)
    return res


def get_prime_bits(num, primes):
    res = 0
    for i, p in enumerate(primes):
        if num % p == 0:
            res ^= 1 << i
    return res


class Solution:
    def numberOfGoodSubsets(self, nums: List[int]) -> int:
        primes = get_primes(max(nums))

        # get rid of ones and numbers that have repeating prime divisors
        num_ones = nums.count(1)
        nums = [num for num in nums if num > 1 and all(num % (p**2) != 0 for p in primes)]
        
        counter = {get_prime_bits(num, primes): count for num, count in Counter(nums).items()}
        nums = sorted(counter.keys())

        @cache
        def num_subsets(i, prime_bits):
            if i == len(nums):
                return prime_bits > 0

            cur_num = nums[i]
            # not including cur_num
            res = num_subsets(i + 1, prime_bits) % MOD
            if prime_bits & cur_num == 0:
                # including cur_num
                res += counter[cur_num] * num_subsets(i + 1, prime_bits | cur_num)
                res %= MOD
            return res

        return (num_subsets(0, 0) * (2 ** num_ones % MOD)) % MOD

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