desgin a circuit using $15$ gates or less $,$ with $5$ inputs $($a$,$b$,$c$,$d$,$e$)$and $3$ outputs $($x$,$y$,$z$).$ output is equal to numbers of $1\text{'}$s in input in binary with these possible output

$001$

$010$

$011$

$100$

$101,$ I already found z $,$ Z$=$ A xor B xor C xor D xor E