<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 __init__(self):
        self.goodnum = [2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30]
        self.sgoodnum = set(self.goodnum)
        self.goodset = set([])
        @cache
        def dfs(i,mask):
            self.goodset.add(mask)
            if i == len(self.goodnum):
                return 
            dfs(i+1,mask)
            possible = True
            for j in range(i):
                if mask & (1<<j):
                    if gcd(self.goodnum[i],self.goodnum[j]) > 1:
                        possible = False
                        break
            if possible:
                dfs(i+1,mask | (1<<i))
        dfs(0,0)
    def numberOfGoodSubsets(self, nums: List[int]) -> int:
        ones = nums.count(1)
        res0 = pow(2,ones,10**9+7) - 1
        res1 = 0
        nums = [n for n in nums if n in self.goodnum]
        freq = Counter(nums)
        for mask in self.goodset:
            curr = 0
            for i in range(18):
                if not mask & (1 << i):
                    continue
                if self.goodnum[i] not in freq:
                    curr = 0
                    break
                else:
                    if curr:
                        curr *= freq[self.goodnum[i]] % (10**9+7)
                    else:
                        curr = freq[self.goodnum[i]] % (10**9+7)
            res1 += curr
        if not res1:
            return 0
        if not res0:
            return res1 % (10**9+7)
        return (res0+1)*res1 % (10**9+7)
1889