3. Let $A=\{1,2,3,4,5\}$. Then the number of mappings $f: A \rightarrow A$ that satisfy the condition $f(f(x))$ $=f(x)$ is $\qquad$ (answer with a number)
3.196 .

It can be generalized to the case where $A$ has $n$ elements. From the condition, if $a \in A$ and $a$ is in the range of $f$, then it must be that $f(a)=a$. Therefore, we can classify $f$ based on the number of elements in its range. The number of $f$ with $k\left(k \in \mathbf{N}_{+}\right)$ elements in its range is $\mathrm{C}_{n}^{k} k^{n-k}$. Hence, the number of $f$ that satisfy the condition is $\sum_{k=1}^{n} \mathrm{C}_{n}^{k} k^{n-k}$. Taking $n=5$ yields the result.