fix this $[$the error $($if there is any$)]$ and add the messing things according to this:

A company has set up software to track its products. All the company's staff can consult the system, either to check that a product exists, or to browse freely through the information. Any consultation must be preceded by a light authentication in which the person specifies their name and department. Engineers can carry out several updating operations for products $($adding$,$ removing, modifying$).$ These operations must be preceded by a more thorough authentication, in which the engineer specifies his or her name and department and enters a password, which is verified by contacting the personnel management system. All operations $($consultation and updating$)$ are recorded in an access log and can optionally be accompanied by a printout of the documents for the director.

Question: Give a use case diagram to model the above problem