<p>A valid parentheses string is either empty <code>&quot;&quot;</code>, <code>&quot;(&quot; + A + &quot;)&quot;</code>, or <code>A + B</code>, where <code>A</code> and <code>B</code> are valid parentheses strings, and <code>+</code> represents string concatenation.</p>

<ul>
	<li>For example, <code>&quot;&quot;</code>, <code>&quot;()&quot;</code>, <code>&quot;(())()&quot;</code>, and <code>&quot;(()(()))&quot;</code> are all valid parentheses strings.</li>
</ul>

<p>A valid parentheses string <code>s</code> is primitive if it is nonempty, and there does not exist a way to split it into <code>s = A + B</code>, with <code>A</code> and <code>B</code> nonempty valid parentheses strings.</p>

<p>Given a valid parentheses string <code>s</code>, consider its primitive decomposition: <code>s = P<sub>1</sub> + P<sub>2</sub> + ... + P<sub>k</sub></code>, where <code>P<sub>i</sub></code> are primitive valid parentheses strings.</p>

<p>Return <code>s</code> <em>after removing the outermost parentheses of every primitive string in the primitive decomposition of </em><code>s</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;(()())(())&quot;
<strong>Output:</strong> &quot;()()()&quot;
<strong>Explanation:</strong> 
The input string is &quot;(()())(())&quot;, with primitive decomposition &quot;(()())&quot; + &quot;(())&quot;.
After removing outer parentheses of each part, this is &quot;()()&quot; + &quot;()&quot; = &quot;()()()&quot;.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;(()())(())(()(()))&quot;
<strong>Output:</strong> &quot;()()()()(())&quot;
<strong>Explanation:</strong> 
The input string is &quot;(()())(())(()(()))&quot;, with primitive decomposition &quot;(()())&quot; + &quot;(())&quot; + &quot;(()(()))&quot;.
After removing outer parentheses of each part, this is &quot;()()&quot; + &quot;()&quot; + &quot;()(())&quot; = &quot;()()()()(())&quot;.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;()()&quot;
<strong>Output:</strong> &quot;&quot;
<strong>Explanation:</strong> 
The input string is &quot;()()&quot;, with primitive decomposition &quot;()&quot; + &quot;()&quot;.
After removing outer parentheses of each part, this is &quot;&quot; + &quot;&quot; = &quot;&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[i]</code> is either <code>&#39;(&#39;</code> or <code>&#39;)&#39;</code>.</li>
	<li><code>s</code> is a valid parentheses string.</li>
</ul>