Consider a search space, where each state can be a city, suburb, farmland, or mountain. The goal is to reach any state that is a mountain. Here are some rules on the successors of different states:

Successors of a city are always suburbs.

Each city has at least one suburb as a successor.

Successors of a suburb can only be cities, or suburbs, or farms.

Each suburb has at least one city as a successor.

Successors of a farm can only be farms, or suburbs, or mountains.

Each farm has at least one other farm as a successor.

Successors of a mountain can only be farms.

Define the best admissible heuristic h you can define using only the above information (you should not assume knowledge of any additional information about the state space). By "best admissible" we mean that h(n) is always the highest possible value we can give, while ensuring that heuristic h is still admissible. You should assume that every move from one state to another has cost 1.