<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> <p> </p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> ideas = ["coffee","donuts","time","toffee"] <strong>Output:</strong> 6 <strong>Explanation:</strong> The following selections are valid: - ("coffee", "donuts"): The company name created is "doffee conuts". - ("donuts", "coffee"): The company name created is "conuts doffee". - ("donuts", "time"): The company name created is "tonuts dime". - ("donuts", "toffee"): The company name created is "tonuts doffee". - ("time", "donuts"): The company name created is "dime tonuts". - ("toffee", "donuts"): The company name created is "doffee tonuts". Therefore, there are a total of 6 distinct company names. The following are some examples of invalid selections: - ("coffee", "time"): The name "toffee" formed after swapping already exists in the original array. - ("time", "toffee"): Both names are still the same after swapping and exist in the original array. - ("coffee", "toffee"): Both names formed after swapping already exist in the original array. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> ideas = ["lack","back"] <strong>Output:</strong> 0 <strong>Explanation:</strong> There are no valid selections. Therefore, 0 is returned. </pre> <p> </p> <p><strong>Constraints:</strong></p> <ul> <li><code>2 <= ideas.length <= 5 * 10<sup>4</sup></code></li> <li><code>1 <= ideas[i].length <= 10</code></li> <li><code>ideas[i]</code> consists of lowercase English letters.</li> <li>All the strings in <code>ideas</code> are <strong>unique</strong>.</li> </ul>