Problem Statement

Given a string s, return the total number of unique palindromes of length 3 which are subsequences of s. Even if multiple ways exist to obtain the same subsequence, it is still only counted once.

A palindrome string is a sequence of characters that reads the same backward as forward.

A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.

Examples

Example 1:

• Input: s = "abcba"
• Expected Output: 3
• Justification: The three unique length-3 palindromic subsequences are "aba", "aca", and "bcb".

Example 2:

• Input: s = "aba"
• Expected Output: 1
• Justification: The one unique length-3 palindromic subsequence is "aba".

Example 3:

• Input: s = "aacbbcacb"
• Expected Output: 9
• Justification: The nine unique length-3 palindromic subsequences are "aaa", "aca", "aba", "ccc", "cbc", "bbb", "bab", "cac", and "bcb".

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