Question $1-$Constraint Satisfaction Problems $(5$ points$)$

Consider the graph with $8$ nodes A$1,$ A$2,$ A$3,$ A$4,$ H$,$ T$,$ F$1,$ F$2.$ Ai is connected to Ai$+1$ for all i$,$

each Ai is connected to H$,$ H is connected to T$,$ and T is connected to each Fi$.$ Find a $3-$coloring

of this graph by hand using the following strategy: backtracking with conflict$-$directed

backjumping, the variable order A$1,$ H$,$ A$4,$ F$1,$ A$2,$ F$2,$ A$3,$ T$,$ and the value order R$,$ G$,$ B$.$