Consider a circuit with these Boolean outputs:

x

$|$

y

$|$

z

$|$

output

$0$

$|$

$0$

$|$

$0$

$|$

$1$

$0$

$|$

$0$

$|$

$1$

$|$

$1$

$0$

$|$

$1$

$|$

$0$

$|$

$0$

$0$

$|$

$1$

$|$

$1$

$|$

$0$

$1$

$|$

$0$

$|$

$0$

$|$

$1$

$1$

$|$

$0$

$|$

$1$

$|$

$1$

$1$

$|$

$1$

$|$

$0$

$|$

$0$

$1$

$|$

$1$

$|$

$1$

$|$

$0$

How many gates are needed if the gates may have $1,2,$ or $3$ inputs after simplification of the corresponding Boolean expression?