Consider the following logic circuit

Write that resulting equivalent Boolean expression for $Z$ as a Product of Sums $($PoS$)$

Hints:

Remember the Pos for a $4$ to $1$ Mux

$(10+C+D)(11+C+D^{\text{'}})(12+C^{\text{'}}+D)(13+C^{\text{'}}+D^{\text{'}})=z$

Remember that the NAND gate can be expressed as

$(A^{-}B{)}^{\text{'}}=A^{\text{'}}+B^{\text{'}}$

Remember that Exclusive$-$Or $($XOR$)$ can be expressed as

$Ao+B=A{B}^{\text{'}}+A^{\text{'}}B=(A+B)(A^{\text{'}}+B^{\text{'}})$

Your answer doesn't have to be optimal. However, it must be expressed appropriately as a PoS with inputs A$,$ B$,$ C$.$ D$.$ Write your answer with no spaces.