Count inversions in a permutation

## Problem Given an array `a` of length `n` that is a permutation of distinct integers (e.g., `1..n`), define an **inversion** as a pair of indices `(i, j)` such that: - `0 ≤ i < j < n`, and - `a[i] > a[j]`. ### Task Write a function that returns the number of inversions in the array. ### Input/Output - **Input:** an integer array `a` with all distinct values - **Output:** a single integer = the number of inversions ### Notes - Any time complexity is acceptable (e.g., an `O(n^2)` approach is fine), but you may also discuss faster approaches if you know them.