<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:
        primes = [False, False ] + [True]*29
        for i in range(2, int(sqrt(31)) + 1):
            if primes[i]:
                for multiple in range(i*i, 31, i):
                    primes[multiple] = False
        
        primeOffset = defaultdict(int)
        index = 0
        for i, value in enumerate(primes):
            if value:
                primeOffset[i] = index

            index +=1

        @lru_cache(None)
        def calculatePrimeFactors(num):
            factors = []
            for i in range(2, int(sqrt(num)) + 1):
                while num % i == 0:
                    factors.append(i)
                    num //= i

            if  2 <= num:
                factors.append(num)

            if len(factors) > 0 and len(set(factors)) == len(factors):
                return factors

            return None

        counter = defaultdict(int)
        factors = defaultdict(list)
        for num in nums:
            counter[num] += 1
            if not num in factors:
                curr = calculatePrimeFactors(num)
                if curr:
                    factors[num] = curr
                
        mod = 10**9 + 7
        n = 31
        @lru_cache(None)
        def dp(val, mask):
            if val == n:
                if mask == 0:
                    return 0

                return 1

            ans = dp(val + 1, mask)
            if val in factors:
                newMask = mask
                shouldInclude = True
                for factor in factors[val]:
                    offset = primeOffset[factor]
                    if (mask >> offset) & 1 == 1:
                        shouldInclude = False
                        break

                    newMask = newMask | (1 << offset)
            
                if shouldInclude:
                    ans += counter[val]*dp(val + 1, newMask)

            return ans%mod

        ans = dp(0,0)
        return (ans + (2**counter[1] - 1)*ans%mod)%mod

            


            
1643