You are designing a heuristic to use with A$*$ search for a navigation problem. Every location in the problem has a unique color assigned to it$.$

$$ The Goal location and any location that is less than $30$ miles away from it is colored Red.

$$ Any location that is colored Yellow is $30$ miles or more away from the Goal location $($but it is less than $50$ miles away$).$

$$ A Location that is colored Blue is more than $50$ miles away from the Goal and atleast $40$ miles away from a location that is colored

Yellow.

$$ A Location that is colored Green is more than $50$ miles away from the Goal but is less than $40$ miles away from a location that is colored Yellow.

$$ All Locations colored Black are atleast $100$ miles away from the Goal.

Note: All distances are discrete values $($you do not have to worry about values less than $1$ mile$)$

Based on the given information give a maximally admissible heuristic that uses the color of a location to estimate distance from that location to the goal.