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, $1-405$ services $1-5,$ and $1-290$ services $1-90.$ 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$.$

or any number not between $1$ and $999,$ the output is:

$0$ is not a valid interstate highway number.

$200$

the output is:

$200$ is not a valid interstate highway number.

See Wikipedia for more info on highway numbering

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