Beautiful Pairs

You are given a sequence $A_1, A_2, \ldots, A_N$. An ordered pair of indices $(i,j)$ in this sequence is called a *beautiful pair* if $i \neq j$ and $\frac{A_i - A_j}{A_i} \lt \frac{A_i - A_j}{A_j}$. (Here, division represents real division, e.g. $\frac{5}{2}$ is equal to $2.50$.) Help Chef find the number of beautiful pairs present in the given sequence. **Note:** Since the input is large, pref