GATE | GATE CS 2019 | Question 57

Let Σ be the set of all bijections from {1, ..., 5} to {1, ..., 5}, where id denotes the identity function, i.e. id(j) = j,∀j. Let ° denote composition on functions. For a string x = x₁x₂ ... x_n ∈ Σn, n ≥ 0, let π(x) = x₁°x₂° ... °x_n. Consider the language L = {x ∈ Σ* ⏐ π(x) = id}. The minimum number of states in any DFA accepting L is _________ .
Note: This was Numerical Type question.