Consider the map coloring problem shown in class (coloring Australia re- gions). Remove Tasmania (T) from the problem because it is independent. Assume that the variable ordering is SA WA NT Q NSW V, and the value ordering is red - green - blue. 3a) Using backtracking with forward checking, find the first solution found when you start with assigning SA-red. Show your search in the same manner as in the lecture slides, that is, show for each row the legal values of each remaining variable. Use "r", "g" and "b" to denote legal values and "red", "green" and "blue" to denote assigned values. How many variables were assigned values before you found the solution? 3b) Consider the same problem again, except that it is now an optimization problem, where you have a preference for the colors used. Specifically, you prefer red over green, and green over blue. Model this optimization problem as a constraint optimization prob- lem (COP). In other words, what are the variables, domains, and constraints (also known as cost functions)? Also provide an optimal solution to your problem 3c) Finally, imagine that Australia is divided into two autonomous coun- tries - East Australia and West Australia. East Australia is composed of Western Australia, Northern Territory, and South Australia regions; and West Australia is composed of Queensland, New South Wales, and Victoria regions. Each country has its own map coloring authority and must coordinate with the authorities of other countries to color their regions The map coloring authority of East Australia strongly prefers red and is indifferent between green and blue The map coloring authority of West Australia prefers red over green, and green over blue. Additionally, the colors of neighboring regions must be different Model this problem as a distributed constraint optimization problem (DCOP). In other words, what are the agents, variables, domains, con- straints (also known as cost functions), and mapping function of vari- ables to agents? Also provide an optimal solution to your