<p>You are given an array of strings <code>ideas</code> that represents a list of names to be used in the process of naming a company. The process of naming a company is as follows:</p>
<ol>
<li>Choose 2 <strong>distinct</strong> names from <code>ideas</code>, call them <code>idea<sub>A</sub></code> and <code>idea<sub>B</sub></code>.</li>
<li>Swap the first letters of <code>idea<sub>A</sub></code> and <code>idea<sub>B</sub></code> with each other.</li>
<li>If <strong>both</strong> of the new names are not found in the original <code>ideas</code>, then the name <code>idea<sub>A</sub> idea<sub>B</sub></code> (the <strong>concatenation</strong> of <code>idea<sub>A</sub></code> and <code>idea<sub>B</sub></code>, separated by a space) is a valid company name.</li>
<li>Otherwise, it is not a valid name.</li>
</ol>
<p>Return <em>the number of <strong>distinct</strong> valid names for the company</em>.</p>
