$(12$ points$)$ Design a combinational circuit with three inputs X$,$ Y$,$ Z and three outputs A$,$ B$,$ C$.$

When the binary input is $0$ or $7,$ the binary output is the same as the input.

When the binary input is $1,2,$ or $3,$ the binary output is two more than the input.

When the binary input is $4,5,$ or $6,$ the binary output is one less than the input.

The three input bits and the three output bits each represent binary numbers.

Use the given signal names $($A$,$ B$,$ C$,$ X$,$ Y$,$ Z$)$ in your solution.