First Element Counting

You are given an array $A$ of $N$ **distinct** integers: $[A_1, A_2, \ldots, A_N]$. We define $f(X)$ as the index $i$ which has the minimum value of $|A_i - X|$ among $i = 1, 2, \ldots, N$. In case there are multiple indices $i$ with the minimum value, choose the one with the smallest value of $A_i$. Your task is to count the number of integers $X$ such that $f(X) = i$ for each $i = 1, 2, \ldots