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<p>You are given a string <code>s</code>. Reorder the string using the following algorithm:</p>
<ol>
<li>Pick the <strong>smallest</strong> character from <code>s</code> and <strong>append</strong> it to the result.</li>
<li>Pick the <strong>smallest</strong> character from <code>s</code> which is greater than the last appended character to the result and <strong>append</strong> it.</li>
<li>Repeat step 2 until you cannot pick more characters.</li>
<li>Pick the <strong>largest</strong> character from <code>s</code> and <strong>append</strong> it to the result.</li>
<li>Pick the <strong>largest</strong> character from <code>s</code> which is smaller than the last appended character to the result and <strong>append</strong> it.</li>
<li>Repeat step 5 until you cannot pick more characters.</li>
<li>Repeat the steps from 1 to 6 until you pick all characters from <code>s</code>.</li>
</ol>
<p>In each step, If the smallest or the largest character appears more than once you can choose any occurrence and append it to the result.</p>
<p>Return <em>the result string after sorting </em><code>s</code><em> with this algorithm</em>.</p>
<p>&nbsp;</p>
<p><strong>Example 1:</strong></p>
<pre>
<strong>Input:</strong> s = &quot;aaaabbbbcccc&quot;
<strong>Output:</strong> &quot;abccbaabccba&quot;
<strong>Explanation:</strong> After steps 1, 2 and 3 of the first iteration, result = &quot;abc&quot;
After steps 4, 5 and 6 of the first iteration, result = &quot;abccba&quot;
First iteration is done. Now s = &quot;aabbcc&quot; and we go back to step 1
After steps 1, 2 and 3 of the second iteration, result = &quot;abccbaabc&quot;
After steps 4, 5 and 6 of the second iteration, result = &quot;abccbaabccba&quot;
</pre>
<p><strong>Example 2:</strong></p>
<pre>
<strong>Input:</strong> s = &quot;rat&quot;
<strong>Output:</strong> &quot;art&quot;
<strong>Explanation:</strong> The word &quot;rat&quot; becomes &quot;art&quot; after re-ordering it with the mentioned algorithm.
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>
<ul>
<li><code>1 &lt;= s.length &lt;= 500</code></li>
<li><code>s</code> consists of only lowercase English letters.</li>
</ul>