Please solve the programming task below using a self-contained code snippet in a markdown code block.

Given a string s, return the number of unique palindromes of length three that are a subsequence of s.
Note that even if there are multiple ways to obtain the same subsequence, it is still only counted once.
A palindrome is a string that reads the same forwards and backwards.
A subsequence of a string is a new string generated from the original string with some characters (can be none) deleted without changing the relative order of the remaining characters.

For example, "ace" is a subsequence of "abcde".

 
Please complete the following python code precisely:
```python
class Solution:
    def countPalindromicSubsequence(self, s: str) -> int:
```