<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:
        '''
        1 <= nums[i] <= 30


        bitmask?
        
        distinct prime numbers
        '''
        MOD = 10 ** 9 + 7
        primes = set({2, 3, 5, 7, 11, 13, 17, 19, 23, 29})
        mask = defaultdict(int)
        
        for index, num in enumerate([2, 3, 5, 7, 11, 13, 17, 19, 23, 29]):
            mask[num] = 1 << index
            
        
        mask_of_num = defaultdict(int)
        
        options = []
        
        for n in nums:
            start = 0
            
            check = True
            for p in primes:
    
                
                if n % (p ** 2) == 0:  
                    check = False
                    break
                        
                if n % p == 0:
                    start |= mask[p]
                    
            if check:
                mask_of_num[n] = start
                options.append(n)
                
            
        N = len(options)
        c = Counter(options)

        @cache
        def calc(x, m):
            if x == 31:
                return int(m != 0)

            best = calc(x + 1, m)

            if c[x]:
                if x == 1:
                    # choose to include or not include c[s] 1's
                    best *= 2 ** c[x]
                
                elif m & mask_of_num[x] == 0:
                    # include 1 of the x c[x] times
                    best += c[x] * calc(x + 1, m | mask_of_num[x])

            return best % MOD
        
        return calc(1, 0) % MOD
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