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"categoryTitle": "Algorithms",
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"title": "Count the Number of Square-Free Subsets",
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"content": "<p>You are given a positive integer <strong>0-indexed</strong>&nbsp;array <code>nums</code>.</p>\n\n<p>A subset of the array <code>nums</code> is <strong>square-free</strong> if the product of its elements is a <strong>square-free integer</strong>.</p>\n\n<p>A <strong>square-free integer</strong> is an integer that is divisible by no square number other than <code>1</code>.</p>\n\n<p>Return <em>the number of square-free non-empty subsets of the array</em> <strong>nums</strong>. Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p>A <strong>non-empty</strong>&nbsp;<strong>subset</strong> of <code>nums</code> is an array that can be obtained by deleting some (possibly none but not 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 class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [3,4,4,5]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> There are 3 square-free subsets in this example:\n- The subset consisting of the 0<sup>th</sup> element [3]. The product of its elements is 3, which is a square-free integer.\n- The subset consisting of the 3<sup>rd</sup> element [5]. The product of its elements is 5, which is a square-free integer.\n- The subset consisting of 0<sup>th</sup> and 3<sup>rd</sup> elements [3,5]. The product of its elements is 15, which is a square-free integer.\nIt can be proven that there are no more than 3 square-free subsets in the given array.</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> There is 1 square-free subset in this example:\n- The subset consisting of the 0<sup>th</sup> element [1]. The product of its elements is 1, which is a square-free integer.\nIt can be proven that there is no more than 1 square-free subset in the given array.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length&nbsp;&lt;= 1000</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 30</code></li>\n</ul>\n",
"translatedTitle": "无平方子集计数",
"translatedContent": "<p>给你一个正整数数组 <code>nums</code> 。</p>\n\n<p>如果数组 <code>nums</code> 的子集中的元素乘积是一个 <strong>无平方因子数</strong> ,则认为该子集是一个 <strong>无平方</strong> 子集。</p>\n\n<p><strong>无平方因子数</strong> 是无法被除 <code>1</code> 之外任何平方数整除的数字。</p>\n\n<p>返回数组 <code>nums</code> 中 <strong>无平方</strong> 且 <strong>非空</strong> 的子集数目。因为答案可能很大,返回对 <code>10<sup>9</sup> + 7</code> 取余的结果。</p>\n\n<p><code>nums</code> 的 <strong>非空子集</strong> 是可以由删除 <code>nums</code> 中一些元素(可以不删除,但不能全部删除)得到的一个数组。如果构成两个子集时选择删除的下标不同,则认为这两个子集不同。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<pre>\n<strong>输入:</strong>nums = [3,4,4,5]\n<strong>输出:</strong>3\n<strong>解释:</strong>示例中有 3 个无平方子集:\n- 由第 0 个元素 [3] 组成的子集。其元素的乘积是 3 ,这是一个无平方因子数。\n- 由第 3 个元素 [5] 组成的子集。其元素的乘积是 5 ,这是一个无平方因子数。\n- 由第 0 个和第 3 个元素 [3,5] 组成的子集。其元素的乘积是 15 ,这是一个无平方因子数。\n可以证明给定数组中不存在超过 3 个无平方子集。</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre>\n<strong>输入:</strong>nums = [1]\n<strong>输出:</strong>1\n<strong>解释:</strong>示例中有 1 个无平方子集:\n- 由第 0 个元素 [1] 组成的子集。其元素的乘积是 1 ,这是一个无平方因子数。\n可以证明给定数组中不存在超过 1 个无平方子集。</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&nbsp;&lt;= 1000</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 30</code></li>\n</ul>\n",
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"Label primes from {2, 3, … 29} with {0,1, … 9} and let DP(i, mask) denote the number of subsets before index: i with the subset of taken primes: mask.",
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