Primary U$.$S$.$ interstate highways are numbered $1-99.$ Odd numbers $($like the $5$ or $95)$ go north$/$south$,$ and evens $($like the $10$ or $90)$ go east$/$west$.$ Auxiliary highways are numbered $100-999,$ and service the primary highway indicated by the rightmost two digits. Thus, I$-405$ services I$-5,$ and I$-290$ services I$-90.$ Note: $200$ is not a valid auxiliary highway because $00$ is not a valid primary highway number.

Given a highway number, indicate whether it is a primary or auxiliary highway. If auxiliary, indicate what primary highway it serves. Also indicate if the $($primary$)$ highway runs north$/$south or east$/$west$.$

Ex: If the input is:

$90$

the output is:

I$-90$ is primary, going east$/$west$.$

Ex: If the input is:

$290$

the output is:

I$-290$ is auxiliary, serving I$-90,$ going east$/$west$.$

Ex: If the input is:

$0$

the output is:

$0$ is not a valid interstate highway number.

Ex: If the input is:

$200$

the output is:

$200$ is not a valid interstate highway number.