Problem - Global and Local Inversions

Given an integer array $A$ of length $n$, return true if the number of global inversions equals the number of local inversions.

A global inversion is a pair $(i, j)$ where $i < j$ and $A[i] > A[j]$. A local inversion is an index $i$ where $A[i] > A[i + 1]$. Every local inversion is a global inversion.

The question asks: are all global inversions local? Use BIT to count global inversions, then check if it equals the local count. Constraints: $n$ up to $10^5$.