Counting Binary Substrings (Backend)

A substring is a group of contiguous characters in a string. For instance, all substrings of abc are [a, b, c, ab, bc, abc].

Given a binary representation of a number, determine the total number of substrings present that match the following conditions:

• The 0s and 1s are grouped consecutively (e.g., 01, 10, 0011, 1100, 000111, etc.).
• The number of 0s in the substring is equal to the number of 1s in the substring.

As an example, consider the string 001101. The 4 substrings matching the two conditions include [0011, 01, 10, 01]. Note that 01 appears twice, from indices 1-2 and 4-5. There are other substrings, e.g. 001 and 011 that match the first condition but not the second.