PROBLEM $\backslash$#$2(30$ points$)$ Combinatorial Testing $($All$-$Pairs testing$)$

An application under development can be installed on different platforms with different display capabilities. Before installing the application on a specific platform three $(3)$ input parameters $($input variables$)$ need to be set: Display Mode, Fonts, Screen Size. The following are possible values of input parameters:

There are $24$ possible configurations of the application that would need to be tested. However, to reduce the cost of testing it was decided to use Pair$-$Wise testing $($All$-$Pairs testing$)$ to significantly reduce the number of configurations to be tested, i$.$e$.,$ the number of configurations to be tested should be at most $12$ configurations.

In this problem, design a set of test cases $($configurations$)$ that satisfy the Pair$-$Wise testing $($All Pairs testing$).$ Show that your all tests satisfy the requirements of the Pair$-$Wise testing.

Note: Sample tests$/$configurations:

Test $\backslash$#$1$: Display Mode $\backslash (=$G $\backslash ),$ Fonts $\backslash (=$S $\backslash ),$ Screen Size $\backslash (=$H $\backslash )$

Test $\backslash$#$2$: Display Mode $\backslash (=$T $\backslash ),$ Fonts $\backslash (=$M $\backslash ),$ Screen Size $\backslash (=$F $\backslash )$