2306. Naming a Company
Hard
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You are given an array of strings `ideas` 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:

1. Choose 2 distinct names from `ideas`, call them `ideaA` and `ideaB`.
2. Swap the first letters of `ideaA` and `ideaB` with each other.
3. If both of the new names are not found in the original `ideas`, then the name `ideaA ideaB` (the concatenation of `ideaA` and `ideaB`, separated by a space) is a valid company name.
4. Otherwise, it is not a valid name.

Return the number of distinct valid names for the company.

Example 1:

```Input: ideas = ["coffee","donuts","time","toffee"]
Output: 6
Explanation: 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.
```

Example 2:

```Input: ideas = ["lack","back"]
Output: 0
Explanation: There are no valid selections. Therefore, 0 is returned.
```

Constraints:

• `2 <= ideas.length <= 5 * 104`
• `1 <= ideas[i].length <= 10`
• `ideas[i]` consists of lowercase English letters.
• All the strings in `ideas` are unique.
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