Given a string s, return the number of distinct nonempty palindromic subsequences in s.

Since the answer can be very large, return it modulo $10^9 + 7$.

A subsequence of a string is obtained by deleting zero or more characters from the original string without altering the relative order of the remaining characters.

A string is palindromic if it reads the same forwards and backwards.

Two subsequences are considered distinct if their string values are different.

Constraints:

• $1 \leq$ s.length $\leq 1000$

• s[i] is either 'a', 'b', 'c', or 'd'.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.