Unique Length-3 Palindromic Subsequences

lcpy gen -n 1930   # by problem number
lcpy gen -s unique_length_3_palindromic_subsequences   # by problem name

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")

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

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")

class Solution:
    # Time: O(26 * n)
    # Space: O(1)
    def count_palindromic_subsequence(self, s: str) -> int:
        total = 0
        for outer in set(s):
            left = s.index(outer)
            right = s.rindex(outer)
            if left == right:
                continue
            total += len(set(s[left + 1 : right]))
        return total