I need to write a shell log rotation script. The requirements are below.

1. The script must be a single file.
2. Script must rotate /var/log/messages
3. Archived log files should be date+timestamped and compressed in a .tar.gz
4. Rotation should occur every hour on the hour.
5. Files older than 7 hours should be deleted.
6. Permissions for the archived files should be root rw-rr
7. The group should be root:nobody
8. Every command in the script should be explained in a comment.
9. Cannot use the logrotate command, logrotated, or any log rotation software.