Design a circuit with a $3-$bit input and $3-$bit output that does the following:

$$ if the input is an even number $<4$; the output $=$ input $+2$

$$ if the input is an even number $>4$; the output $=$ input $+4$

$$ if the input is an odd number; the output $=$ input $1$

$$ note: you may consider $0$ to be an even number for this problem.