<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:
        arr = [2,3,5,7,11,13,17,19,23,29]
        def solve(num):
            curr = 0
            for idx,i in enumerate(arr):
                cnt = 0
                while num%i == 0:
                    num = num//i
                    cnt +=1
                if cnt > 1:
                    return -1
                if cnt:
                    curr = curr|(1<<idx)
            return curr if curr != 0 else -1
        go = lambda x,y:bin(x).count("1")+bin(y).count("1") == bin(x|y).count("1")
        freq = {}
        for i in nums:
            freq[i] = 1+freq.get(i,0)
        temp = [(solve(i),i) for i in range(2,31) if solve(i) != -1]
        h = defaultdict(list)
        ans = -1
        mod = 10**9 + 7
        def helper(i,curr, res):
            nonlocal ans
            if i == len(temp):
                goto = 1
                for j in res:
                    goto *= freq.get(j,0)
                    goto %= mod
                ans += goto
                ans %= mod
                return
            if go(curr, temp[i][0]):
                res.append(temp[i][1])
                helper(i+1, curr|temp[i][0], res)
                res.pop()
            helper(i+1, curr, res) 
        helper(0,0,[])
        return (ans*(pow(2, freq.get(1, 0), mod)))%mod
1716