Crazy Substrings

Gotham City is the home of Batman, and Batman likes to keep his people together. There are $N$ houses in the city. The resident of the $i^{th}$ house is of type $A_i$. It is known that people of the same type are friends and people of different types are not friends. To maintain peace, Batman can do the following type of operation: - Choose indices $i$ and $j$ $(1\leq i \le j \le N)$ and rever