Question 90
Let $A=\{1,2, \ldots, n\}, n \geq 4$. For any function $f: A \rightarrow A$ and any $a \in A$ define $f_{1}(a)=f(a)$, $f_{i+1}(a)=f\left(f_{i}(a)\right)$, $i \geq 1$. Find the number of the functions $f$ such that $f_{n-2}$ is a constant function but $f_{n-3}$ is not.