<p>Given a string <code>s</code> consisting only of characters <code>&#39;a&#39;</code>, <code>&#39;b&#39;</code>, and <code>&#39;c&#39;</code>. You are asked to apply the following algorithm on the string any number of times:</p>

<ol>
	<li>Pick a <strong>non-empty</strong> prefix from the string <code>s</code> where all the characters in the prefix are equal.</li>
	<li>Pick a <strong>non-empty</strong> suffix from the string <code>s</code> where all the characters in this suffix are equal.</li>
	<li>The prefix and the suffix should not intersect at any index.</li>
	<li>The characters from the prefix and suffix must be the same.</li>
	<li>Delete both the prefix and the suffix.</li>
</ol>

<p>Return <em>the <strong>minimum length</strong> of </em><code>s</code> <em>after performing the above operation any number of times (possibly zero times)</em>.</p>

<p>&nbsp;</p>
<p><strong>Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;ca&quot;
<strong>Output:</strong> 2
<strong>Explanation: </strong>You can&#39;t remove any characters, so the string stays as is.
</pre>

<p><strong>Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;cabaabac&quot;
<strong>Output:</strong> 0
<strong>Explanation:</strong> An optimal sequence of operations is:
- Take prefix = &quot;c&quot; and suffix = &quot;c&quot; and remove them, s = &quot;abaaba&quot;.
- Take prefix = &quot;a&quot; and suffix = &quot;a&quot; and remove them, s = &quot;baab&quot;.
- Take prefix = &quot;b&quot; and suffix = &quot;b&quot; and remove them, s = &quot;aa&quot;.
- Take prefix = &quot;a&quot; and suffix = &quot;a&quot; and remove them, s = &quot;&quot;.</pre>

<p><strong>Example 3:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;aabccabba&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong> An optimal sequence of operations is:
- Take prefix = &quot;aa&quot; and suffix = &quot;a&quot; and remove them, s = &quot;bccabb&quot;.
- Take prefix = &quot;b&quot; and suffix = &quot;bb&quot; and remove them, s = &quot;cca&quot;.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 10<sup>5</sup></code></li>
	<li><code>s</code> only consists of characters <code>&#39;a&#39;</code>, <code>&#39;b&#39;</code>, and <code>&#39;c&#39;</code>.</li>
</ul>