<p>An array <code>nums</code> of length <code>n</code> is <strong>beautiful</strong> if:</p>
<ul>
<li><code>nums</code> is a permutation of the integers in the range <code>[1, n]</code>.</li>
<li>For every <code>0 <= i < j < n</code>, there is no index <code>k</code> with <code>i < k < j</code> where <code>2 * nums[k] == nums[i] + nums[j]</code>.</li>
</ul>
<p>Given the integer <code>n</code>, return <em>any <strong>beautiful</strong> array </em><code>nums</code><em> of length </em><code>n</code>. There will be at least one valid answer for the given <code>n</code>.</p>