\item \lect Complete the following python script with the necessary statements. The final script should map each integer of a list of five integers to four possible colours such that the mapping returns different colours for adjacent integers. % You need to declare and populate a z3 \texttt{Datatype} % Furthermore, you need to create a list of five distinct integers and bound them. % Finally, enforce the constraints on the uninterpreted function .... \begin{pythonSourceCode} from itertools import combinations from z3 import * solver = Solver() # Declare a Datatype and populate it with 4 colours. Colours = Datatype("Colours") Colours.declare("RED") Colours.declare("BLUE") Colours.declare("GREEN") Colours.declare("YELLOW") Colour = Colours.create() # Declare a function from integers to your custom datatype f = Function('f', IntSort(), Colour) variables = list() for i in range(0,5): variables.append(Int(i)) # Bound each integer i such that 0 <= i < 5 solver.add(0 <= variables[-1]) solver.add(variables[-1] <= 5) # Enfore that all i are distinct solver.add(Distinct(variables)) # Enforce that colours are different for adjacent integers for combi in combinations(variables,2): solver.add(Implies(Abs(combi[0] - combi[1]) == 1, f(combi[0]) != f(combi[1]))) result = solver.check() if result == sat: print(solver.model()) \end{pythonSourceCode}