Q$1$ Mux

a$)$ Given the below four$-$input boolean function

$F(A,B,C,D)=(A^{\text{'}}+C+D)(B^{\text{'}}+C+D^{\text{'}})(C^{\text{'}}+D)(A+C^{\text{'}}+D^{\text{'}})$

Define the inputs $x0,x1,x2,x3$ to implement the function $F(A,B,C,D)$ using $2$:$1$ multiplexers and NOT gates. Only $1,0,$ A$,$ B$,$ C$,$ D$,$ A$\text{'},$ B$\text{'},$ C$\text{'},$ and D$\text{'}$ are allowed.

$\backslash$table$[[x0,],[x1,],[x2,],[x3,]]$