"content":"<p>You are given a <strong>1</strong><strong>-indexed</strong> array <code>nums</code> of <code>n</code> integers.</p>\n\n<p>A set of numbers is <strong>complete</strong> if the product of every pair of its elements is a perfect square.</p>\n\n<p>For a subset of the indices set <code>{1, 2, ..., n}</code> represented as <code>{i<sub>1</sub>, i<sub>2</sub>, ..., i<sub>k</sub>}</code>, we define its <strong>element-sum</strong> as: <code>nums[i<sub>1</sub>] + nums[i<sub>2</sub>] + ... + nums[i<sub>k</sub>]</code>.</p>\n\n<p>Return <em>the <strong>maximum element-sum</strong> of a <strong>complete</strong> subset of the indices set</em> <code>{1, 2, ..., n}</code>.</p>\n\n<p>A perfect square is a number that can be expressed as the product of an integer by itself.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [8,7,3,5,7,2,4,9]\n<strong>Output:</strong> 16\n<strong>Explanation:</strong> Apart from the subsets consisting of a single index, there are two other complete subsets of indices: {1,4} and {2,8}.\nThe sum of the elements corresponding to indices 1 and 4 is equal to nums[1] + nums[4] = 8 + 5 = 13.\nThe sum of the elements corresponding to indices 2 and 8 is equal to nums[2] + nums[8] = 7 + 9 = 16.\nHence, the maximum element-sum of a complete subset of indices is 16.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [5,10,3,10,1,13,7,9,4]\n<strong>Output:</strong> 19\n<strong>Explanation:</strong> Apart from the subsets consisting of a single index, there are four other complete subsets of indices: {1,4}, {1,9}, {2,8}, {4,9}, and {1,4,9}.\nThe sum of the elements corresponding to indices 1 and 4 is equal to nums[1] + nums[4] = 5 + 10 = 15.\nThe sum of the elements corresponding to indices 1 and 9 is equal to nums[1] + nums[9] = 5 + 4 = 9.\nThe sum of the elements corresponding to indices 2 and 8 is equal to nums[2] + nums[8] = 10 + 9 = 19.\nThe sum of the elements corresponding to indices 4 and 9 is equal to nums[4] + nums[9] = 10 + 4 = 14.\nThe sum of the elements corresponding to indices 1, 4, and 9 is equal to nums[1] + nums[4] + nums[9] = 5 + 10 + 4 = 19.\nHence, the maximum element-sum of a complete subset of indices is 19.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= n == nums.length <= 10<sup>4</sup></code></li>\n\t<li><code>1 <= nums[i] <= 10<sup>9</sup></code></li>\n</ul>\n",
"Let <code>P(x)</code> be the product of all prime numbers <code>p</code> such that <code>p</code> divides <code>x</code>, and there exists an <strong>odd</strong> <code>k</code> such that <code>p^k</code> divides <code>x</code> but <code>p^(k+1)</code> does not.",
"If <code>P(nums[i]) = P(nums[j])</code>, <code>nums[i]</code> and <code>nums[j]</code> can be grouped together.",
"envInfo":"{\"cpp\": [\"C++\", \"<p>Compiled with <code> clang 11 </code> using the latest C++ 20 standard.</p>\\r\\n\\r\\n<p>Your code is compiled with level two optimization (<code>-O2</code>). <a href=\\\"https://github.com/google/sanitizers/wiki/AddressSanitizer\\\" target=\\\"_blank\\\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\"], \"java\": [\"Java\", \"<p><code>OpenJDK 17</code>. Java 8 features such as lambda expressions and stream API can be used. </p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\\r\\n<p>Includes <code>Pair</code> class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.</p>\"], \"python\": [\"Python\", \"<p><code>Python 2.7.12</code>.</p>\\r\\n\\r\\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\\\"https://docs.python.org/2/library/array.html\\\" target=\\\"_blank\\\">array</a>, <a href=\\\"https://docs.python.org/2/library/bisect.html\\\" target=\\\"_blank\\\">bisect</a>, <a href=\\\"https://docs.python.org/2/library/collections.html\\\" target=\\\"_blank\\\">collections</a>. If you need more libraries, you can import it yourself.</p>\\r\\n\\r\\n<p>For Map/TreeMap data structure, you may use <a href=\\\"http://www.grantjenks.com/docs/sortedcontainers/\\\" target=\\\"_blank\\\">sortedcontainers</a> library.</p>\\r\\n\\r\\n<p>Note that Python 2.7 <a href=\\\"https://www.python.org/dev/peps/pep-0373/\\\" target=\\\"_blank\\\">will not be maintained past 2020</a>. For the latest Python, please choose Python3 instead.</p>\"], \"c\": [\"C\", \"<p>Compiled with <code>gcc 8.2</code> using the gnu11 standard.</p>\\r\\n\\r\\n<p>Your code is compiled with level one optimization (<code>-O1</code>). <a href=\\\"https://github.com/google/sanitizers/wiki/AddressSanitizer\\\" target=\\\"_blank\\\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\\r\\n\\r\\n<p>For hash table operations, you may use <a href=\\\"https://troydhanson.github.io/uthash/\\\" target=\\\"_blank\\\">uthash</a>. \\\"uthash.h\\\" is included by default. Below are some examples:</p>\\r\\n\\r\\n<p><b>1. Adding an item to a hash.</b>\\r\\n<pre>\\r\\nstruct hash_entry {\\r\\n int id; /* we'll use this field as the key */\\r\\n char name[10];\\r\\n UT_hash_handle hh; /* makes this structure hashable */\\r\\n};\\r\\n\\r\\nstruct hash_entry *users = NULL;\\r\\n\\r\\nvoid add_user(struct hash_entry *s) {\\r\\n HASH_ADD_INT(users, id, s);\\r\\n}\\r\\n</pre>\\r\\n</p>\\r\\n\\r\\n<p><b>2. Looking up an item in a hash:</b>\\r\\n<pre>\\r\\nstruct hash_entry *find_user(int user_id) {\\r\\n struct hash_entry *s;\\r\\n HASH_FIND_INT(users, &user_id, s);\\r\\n return s;\\r\\n}\\r\\n</pre>\\r\\n</p>\\r\\n\\r\\n<p><b>3. Deleting an item in a hash:</b>\\r\\n<pre>\\r\\nvoid delete_user(struct hash_entry *user) {\\r\\n HASH_DEL(users, user); \\r\\n}\\r\\n</pre>\\r\\n</p>\"], \"csharp\": [\"C#\", \"<p><a href=\\\"https://learn.microsoft.com/en-us/dotnet/csharp/whats-new/csharp-10\\\" target=\\\"_blank\\\">C# 10 with .NET 6 runtime</a></p>\"], \"javascript\": [\"JavaScript\", \"<p><code>Node.js 16.13.2</code>.</p>\\r\\n\\r\\n<p>Your code is run with <code>--harmony</code> flag, enabling <a href=\\\"http://node.green/\\\" target=\\\"_blank\\\">new ES6 features</a>.</p>\\r\\n\\r\\n<p><a href=\\\"https://lodash.com\\\" target=\\\"_blank\\\">lodash.js</a> library is included by default.</p>\\r\\n\\r\\n<p>For Priority Queue / Queue data structures, you may use 5.3.0 version of <a href=\\\"https://github.com/datastructures-js/priority-queue/tree/fb4fdb984834421279aeb081df7af624d17c2a03\\\" target=\\\"_blank\\\">datastructures-js/priority-queue</a> and 4.2.1 version of <a href=\\\"https://githu
