Consider a $100100$ grid world. The agent's task is to get to a goal object. The agent can move to any of its $4$ neighboring locations $($up$,$ down, left and right$)$ by exactly $1$ step. The agent has a sensor that it can use to perceive the brightness its current location. The location with the goal object has a brightness value of $15.$ Locations that are $5$ steps or less away will have a brightness value of $10.$ Locations that are $6$ to $10$ steps away will have a brightness value of $5.$ All other locations will have a brightness value of $0.$

a$)$ Analyze the environment type.

b$)$ Come up with a maximally admissible heuristic which only uses the brightness value from the sensor to estimate the distance to goal from current location.