You are given an array of unique strings ideas representing a collection of candidate names for a company. A valid company name is formed using the following process:

1. Select $2$ distinct words from ideas, denoted as ideaA and ideaB.

2. Swap the first character of ideaA with the first character of ideaB.

3. If both newly created words do not exist in the original ideas array, then the pair forms a valid company name formatted as the first new word followed by a space and the second new word.

4. Otherwise, the pair is considered invalid.

Return the total number of distinct valid company names that can be formed.

Constraints:

• $2 \leq$ ideas.length $\leq 5 imes 10^4$

• $1 \leq$ ideas[i].length $\leq 10$

• ideas[i] consists of lowercase English letters.

• All the strings in ideas are unique.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.