GATE 2019 CS – Question 58

Let $\Sigma$ be the set of all bijections from $\{1,\dots,5\}$ to $\{1,\dots,5\}$, where $id$ denotes the identity function, i.e. $id(j)=j,\forall j$. Let $\circ$ denote composition on functions. For a string $x=x_1x_2\cdots x_n\in\Sigma^n$, $n\ge0$, let $\pi(x)=x_1\circ x_2\circ\cdots\circ x_n$.

Consider the language $L=\{x\in\Sigma^*\mid\pi(x)=id\}$. The minimum number of states in any DFA accepting $L$ is ________.