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"translatedContent": "<p>给你一个长度为&nbsp;<code>n</code>&nbsp;的整数数组&nbsp;<code>nums</code>&nbsp;和一个整数&nbsp;<code>numSlots</code>&nbsp;,满足<code>2 * numSlots &gt;= n</code>&nbsp;。总共有&nbsp;<code>numSlots</code>&nbsp;个篮子,编号为&nbsp;<code>1</code>&nbsp;到&nbsp;<code>numSlots</code>&nbsp;。</p>\n\n<p>你需要把所有&nbsp;<code>n</code>&nbsp;个整数分到这些篮子中,且每个篮子 <strong>至多</strong>&nbsp;有 2 个整数。一种分配方案的 <strong>与和</strong>&nbsp;定义为每个数与它所在篮子编号的 <strong>按位与运算</strong>&nbsp;结果之和。</p>\n\n<ul>\n\t<li>比方说,将数字&nbsp;<code>[1, 3]</code>&nbsp;放入篮子&nbsp;<strong><em><code>1</code></em></strong>&nbsp;中,<code>[4, 6]</code> 放入篮子&nbsp;<strong><em><code>2</code></em></strong>&nbsp;中,这个方案的与和为&nbsp;<code>(1 AND <strong><em>1</em></strong>) + (3 AND <strong><em>1</em></strong>) + (4 AND <em><strong>2</strong></em>) + (6 AND <em><strong>2</strong></em>) = 1 + 1 + 0 + 2 = 4</code>&nbsp;。</li>\n</ul>\n\n<p>请你返回将 <code>nums</code>&nbsp;中所有数放入<em>&nbsp;</em><code>numSlots</code>&nbsp;个篮子中的最大与和。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<pre><b>输入:</b>nums = [1,2,3,4,5,6], numSlots = 3\n<b>输出:</b>9\n<b>解释:</b>一个可行的方案是 [1, 4] 放入篮子 <em><strong>1</strong></em>&nbsp;中,[2, 6] 放入篮子 <strong><em>2</em></strong>&nbsp;中,[3, 5] 放入篮子 <strong><em>3</em></strong> 中。\n最大与和为 (1 AND <strong><em>1</em></strong>) + (4 AND <strong><em>1</em></strong>) + (2 AND <strong><em>2</em></strong>) + (6 AND <strong><em>2</em></strong>) + (3 AND <strong><em>3</em></strong>) + (5 AND <em><strong>3</strong></em>) = 1 + 0 + 2 + 2 + 3 + 1 = 9 。\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre><b>输入:</b>nums = [1,3,10,4,7,1], numSlots = 9\n<b>输出:</b>24\n<b>解释:</b>一个可行的方案是 [1, 1] 放入篮子 <em><strong>1</strong></em> 中,[3] 放入篮子 <em><strong>3</strong></em> 中,[4] 放入篮子 <strong><em>4</em></strong> 中,[7] 放入篮子 <strong><em>7</em></strong> 中,[10] 放入篮子 <strong><em>9</em></strong>&nbsp;中。\n最大与和为 (1 AND <strong><em>1</em></strong>) + (1 AND <strong><em>1</em></strong>) + (3 AND <strong><em>3</em></strong>) + (4 AND <strong><em>4</em></strong>) + (7 AND <strong><em>7</em></strong>) + (10 AND <strong><em>9</em></strong>) = 1 + 1 + 3 + 4 + 7 + 8 = 24 。\n注意篮子 2 5 6 和 8 是空的,这是允许的。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>n == nums.length</code></li>\n\t<li><code>1 &lt;= numSlots &lt;= 9</code></li>\n\t<li><code>1 &lt;= n &lt;= 2 * numSlots</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 15</code></li>\n</ul>\n",
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"hints": [
"Can you think of a dynamic programming solution to this problem?",
"Can you use a bitmask to represent the state of the slots?"