Is it possible to dynamically change the "Save Public Report" option for all interactive reports

I have several hundred reports in an application.

A new requirement is to change the "Save Public Report" setting on all reports.

This is done for new reports but would be a manually setting for existing reports.

Is there a way to dynamically set this option for all reports in apex?

Also what tables are apex reports stored in, in the database?

Thanks,

Conor.