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\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.
# Declare a function from integers to your custom datatype
variables = list()
for i in range(0,5):
variables.append(Int(i))
# Bound each integer i such that 0 <= i < 5
# Enfore that all i are distinct
# Enforce that colours are different for adjacent integers
for combi in combinations(variables,2):
result = solver.check()
if result == sat:
print(solver.model())
\end{pythonSourceCode}