Task $4$: $(10$ points$)$

Consider a search space, where each state can be red, green, blue, yellow, or black. Multiple states

may have the same color. The goal is to reach any black state. Here are some rules on the

successors of different states, based on their color $($these successor functions are unidirectional$)$:

Red states can only have green or blue children

Blue states can only have red or black children

Green states can only have blue or yellow children

Yellow states can only have yellow or red children

Black states can only have green or black children

Define a maximally admissible heuristic that assigns a value to each state based only on the color

of that state. Assume that any move from one state to another has cost $1.$