iRule to rewrite cookie?

Right now, our BigIP is setting a cookie for session persistence. In addition to our main www.example.com site, we have various partner sites in the form of partner1.example.com, partner2.example.com, etc. In each case, the cookie's hostname reflects the partner site, except for our main site, where the hostname just says "example.com" (and not www.example.com).

 

 

What we need is an iRule that changes the way the cookie is set so that its hostname is always "example.com", regardless of the partner site. Any help is very welcome. Thanks!