Birthday Gift Again

All strings in Chefland are beautiful because they are binary strings (a binary string contains only characters '0' and '1'). The *beauty* of a binary string $S$ is defined as the number of pairs $(i, j)$ ($1 \le i \le j \le |S|$) such that the substring $S_i, S_{i+1}, \ldots, S_j$ is special. For a binary string $U$, let's denote the number of occurrences of the characters '1' and '0' in $U$ b