Given a binary string s, partition it into the minimum number of beautiful substrings.

A substring is considered beautiful if:

• It does not contain any leading zeros.

• It is the binary representation of a power of $5$ (such that the value equals $5^k$ for some integer $k \geq 0$).

Return the minimum number of beautiful substrings into which s can be partitioned. If it is impossible to partition s this way, return $-1$.

Constraints:

• $1 \leq$ s.length $\leq 15$

• s[i] is either '0' or '1'.

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.