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52 lines
2.3 KiB
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52 lines
2.3 KiB
HTML
<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>
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<ul>
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<li>For example, if <code>nums = [1, 2, 3, 4]</code>:
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<ul>
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<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>
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<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>
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</ul>
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</li>
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</ul>
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<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>
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<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>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [1,2,3,4]
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<strong>Output:</strong> 6
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<strong>Explanation:</strong> The good subsets are:
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- [1,2]: product is 2, which is the product of distinct prime 2.
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- [1,2,3]: product is 6, which is the product of distinct primes 2 and 3.
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- [1,3]: product is 3, which is the product of distinct prime 3.
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- [2]: product is 2, which is the product of distinct prime 2.
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- [2,3]: product is 6, which is the product of distinct primes 2 and 3.
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- [3]: product is 3, which is the product of distinct prime 3.
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</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [4,2,3,15]
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<strong>Output:</strong> 5
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<strong>Explanation:</strong> The good subsets are:
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- [2]: product is 2, which is the product of distinct prime 2.
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- [2,3]: product is 6, which is the product of distinct primes 2 and 3.
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- [2,15]: product is 30, which is the product of distinct primes 2, 3, and 5.
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- [3]: product is 3, which is the product of distinct prime 3.
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- [15]: product is 15, which is the product of distinct primes 3 and 5.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 <= nums.length <= 10<sup>5</sup></code></li>
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<li><code>1 <= nums[i] <= 30</code></li>
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</ul>
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