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"`.

Example 1:

    Input: s = "aabca"
    Output: 3
    Explanation: The 3 palindromic subsequences of length 3 are:
    - "aba" (subsequence of "aabca")
    - "aaa" (subsequence of "aabca")
    - "aca" (subsequence of "aabca")

Example 2:

    Input: s = "adc"
    Output: 0
    Explanation: There are no palindromic subsequences of length 3 in "adc".

Example 3:

    Input: s = "bbcbaba"
    Output: 4
    Explanation: The 4 palindromic subsequences of length 3 are:
    - "bbb" (subsequence of "bbcbaba")
    - "bcb" (subsequence of "bbcbaba")
    - "bab" (subsequence of "bbcbaba")
    - "aba" (subsequence of "bbcbaba")

Constraints:

- `3 <= s.length <= 105`
- `s` consists of only lowercase English letters.