leetcode-problemset/leetcode-cn/originData/the-number-of-good-subsets.json

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            "title": "The Number of Good Subsets",
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            "content": "<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>\n\n<ul>\n\t<li>For example, if <code>nums = [1, 2, 3, 4]</code>:\n\n\t<ul>\n\t\t<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>\n\t\t<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>\n\t</ul>\n\t</li>\n</ul>\n\n<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>\n\n<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>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,2,3,4]\n<strong>Output:</strong> 6\n<strong>Explanation:</strong> The good subsets are:\n- [1,2]: product is 2, which is the product of distinct prime 2.\n- [1,2,3]: product is 6, which is the product of distinct primes 2 and 3.\n- [1,3]: product is 3, which is the product of distinct prime 3.\n- [2]: product is 2, which is the product of distinct prime 2.\n- [2,3]: product is 6, which is the product of distinct primes 2 and 3.\n- [3]: product is 3, which is the product of distinct prime 3.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [4,2,3,15]\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> The good subsets are:\n- [2]: product is 2, which is the product of distinct prime 2.\n- [2,3]: product is 6, which is the product of distinct primes 2 and 3.\n- [2,15]: product is 30, which is the product of distinct primes 2, 3, and 5.\n- [3]: product is 3, which is the product of distinct prime 3.\n- [15]: product is 15, which is the product of distinct primes 3 and 5.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 30</code></li>\n</ul>\n",
            "translatedTitle": "好子集的数目",
            "translatedContent": "<p>给你一个整数数组&nbsp;<code>nums</code>&nbsp;。如果&nbsp;<code>nums</code>&nbsp;的一个子集中，所有元素的乘积可以表示为一个或多个 <strong>互不相同的质数</strong> 的乘积，那么我们称它为&nbsp;<strong>好子集</strong>&nbsp;。</p>\n\n<ul>\n\t<li>比方说，如果&nbsp;<code>nums = [1, 2, 3, 4]</code>&nbsp;：\n\n\t<ul>\n\t\t<li><code>[2, 3]</code>&nbsp;，<code>[1, 2, 3]</code>&nbsp;和&nbsp;<code>[1, 3]</code>&nbsp;是 <strong>好</strong>&nbsp;子集，乘积分别为&nbsp;<code>6 = 2*3</code>&nbsp;，<code>6 = 2*3</code>&nbsp;和&nbsp;<code>3 = 3</code>&nbsp;。</li>\n\t\t<li><code>[1, 4]</code> 和&nbsp;<code>[4]</code>&nbsp;不是 <strong>好</strong>&nbsp;子集，因为乘积分别为&nbsp;<code>4 = 2*2</code> 和&nbsp;<code>4 = 2*2</code>&nbsp;。</li>\n\t</ul>\n\t</li>\n</ul>\n\n<p>请你返回 <code>nums</code>&nbsp;中不同的&nbsp;<strong>好</strong>&nbsp;子集的数目对<em>&nbsp;</em><code>10<sup>9</sup> + 7</code>&nbsp;<strong>取余</strong>&nbsp;的结果。</p>\n\n<p><code>nums</code>&nbsp;中的 <strong>子集</strong>&nbsp;是通过删除 <code>nums</code>&nbsp;中一些（可能一个都不删除，也可能全部都删除）元素后剩余元素组成的数组。如果两个子集删除的下标不同，那么它们被视为不同的子集。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [1,2,3,4]\n<b>输出：</b>6\n<b>解释：</b>好子集为：\n- [1,2]：乘积为 2 ，可以表示为质数 2 的乘积。\n- [1,2,3]：乘积为 6 ，可以表示为互不相同的质数 2 和 3 的乘积。\n- [1,3]：乘积为 3 ，可以表示为质数 3 的乘积。\n- [2]：乘积为 2 ，可以表示为质数 2 的乘积。\n- [2,3]：乘积为 6 ，可以表示为互不相同的质数 2 和 3 的乘积。\n- [3]：乘积为 3 ，可以表示为质数 3 的乘积。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [4,2,3,15]\n<b>输出：</b>5\n<b>解释：</b>好子集为：\n- [2]：乘积为 2 ，可以表示为质数 2 的乘积。\n- [2,3]：乘积为 6 ，可以表示为互不相同质数 2 和 3 的乘积。\n- [2,15]：乘积为 30 ，可以表示为互不相同质数 2，3 和 5 的乘积。\n- [3]：乘积为 3 ，可以表示为质数 3 的乘积。\n- [15]：乘积为 15 ，可以表示为互不相同质数 3 和 5 的乘积。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 30</code></li>\n</ul>\n",
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