Develop a ladder logic for the following control philosophy:

A separation station works as follows:

$1.$ S $1$ sense the presence $($passage$)$ of a part, to actuate A $1.$ It is to stop the part at the checking station.

$2.$ At the testing station:

a$.$ S$2$ is a retroreflective sensor$.$ It checks if the part provides any reflection. If no reflection is provided, $\backslash ($ A $2\backslash )$ and $\backslash ($ A $3\backslash )$ are not triggered. As such, the part goes to Slide $3$:

b$.$ S$3$ is an inductive sensor to sense only metallic objects. If the part is metallic, A$2$ is triggered. As such, part goes to Slide $1.$ S$4$ is to check if the part entered Slide $1$ and deactivate A$1$:

c$.$ If S $2$ is triggered but S $3$ is not, A $3$ is actuated to send the part to Slide $2.$ S$5$ is to check if the part entered Slide $2$ and deactivate A$3$:

d$.$ The testing process takes $10$ Sec $.$ When the testing is done, A $1$ is deactivated:

Note$1$: the conveyor belt is running constantly.