Problem: Count Prefix and Suffix Pairs

You are given an array of strings called words. Your task is to count the number of pairs (i, j) (where i < j) such that a string words[i] is both a prefix and a suffix of another string words[j].

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Key Definitions:

• Prefix : A string str1 is a prefix of str2 if str2 starts with str1. Example: "ab" is a prefix of "abc", but not of "cab".
• Suffix: A string str1 is a suffix of str2 if str2 ends with str1.
  Example: "bc" is a suffix of "abc", but not of "bca".
• Prefix and Suffix: A string str1 is both a prefix and suffix of str2 if: - str2 starts with str1, and - str2 ends with str1.

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Examples:

Example 1:

Input: words = ["a", "aba", "ababa", "aa"]
Output: 4

Explanation:
The valid pairs (i, j) are:

1. (0, 1) because "a" is both a prefix and suffix of "aba".
2. (0, 2) because "a" is both a prefix and suffix of "ababa".
3. (0, 3) because "a" is both a prefix and suffix of "aa".
4. (1, 2) because "aba" is both a prefix and suffix of "ababa".

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Example 2:

Input: words = ["pa", "papa", "ma", "mama"]
Output: 2

Explanation:
The valid pairs (i, j) are:

1. (0, 1) because "pa" is both a prefix and suffix of "papa".
2. (2, 3) because "ma" is both a prefix and suffix of "mama".

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Example 3:

Input: words = ["abab", "ab"]
Output: 0

Explanation:
No valid pairs exist because none of the strings in words satisfy the condition of being both a prefix and suffix.

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Constraints:

• 1 <= words.length <= 50
• 1 <= words[i].length <= 10
• words[i] contains only lowercase English letters.

Goal:

Return the total number of valid (i, j) pairs where i < j and words[i] is both a prefix and a suffix of words[j].