Write a program using coral$$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:

The $90$ is primary, going east$/$west$.$

Ex: If the input is:

$290$

the output is:

The $290$ is auxiliary, serving the $90,$ going east$/$west$.$

Ex: If the input is:

$0$

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

$0$ is not a valid interstate highway number.

Ex: If the input is:

$411$

the output is:

spring

In addition, check if both integers are valid $($an actual month and day$).$

Ex: If the input is:

$1465$