<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>

class Solution:
    def numberOfGoodSubsets(self, nums: List[int]) -> int:
        max_n = max(nums)
        spf = [1] * (max_n + 1)
        primes = []
        for i in range(2, max_n + 1):
            if spf[i] == 1:
                primes.append(i)
                j = 2
                while i * j <= max_n:
                    if spf[i * j] == 1:
                        spf[i * j] = i
                    j += 1
        d = {p: i for i, p in enumerate(primes)}

        def conv(i):
            mask = 0
            while spf[i] != 1:
                if (1 << d[spf[i]]) & mask: return -1
                mask |= 1 << d[spf[i]]
                i //= spf[i]
            if i != 1:
                if (1 << d[i]) & mask: return -1
                mask |= 1 << d[i]
            return mask

        arr = list(map(conv, nums))
        arr = [i for i in arr if i != -1]
        arr = [(i, ct) for i, ct in Counter(arr).items()]
        @cache
        def dp(i, mask):
            if i == len(arr):
                return int(mask != 0)
            res = dp(i + 1, mask)

            m, ct = arr[i]
            if m == 0:
                res += (2 ** ct - 1) * dp(i + 1, mask)
            elif not mask & m:
                res += ct * dp(i + 1, mask | m)
            return res

        return dp(0, 0) % (10**9 + 7)

1687