Longest Non Decreasing Subsequence

You are given a **binary** string $A$ of length $N$. Let $F(i,j)$ denote the length of **longest non-decreasing** [subsequence](https://en.wikipedia.org/wiki/Subsequence) of the substring $[A_i, A_{i+1}, \ldots, A_j]$. Find the value $\sum_{i=1}^{N} \sum_{j=i}^{N}F(i,j)$. ### Input - The first line of input contains a single integer $T$, denoting the number of test cases. - Each test case consi