Counting users of a role in all network sites

After much searching I have been unable to successfully return a count of users that have a particular role, let say the role is inactive. Ultimately I would like to take the total number of users on the network and subtract the users that have been placed into the inactive role.

To further complicate things, I would like to ensure that this is their only role on the network before they are counted. For example if a person is a member of 2 blogs, their role on both blogs would have to be set to inactive before they are counted as inactive.

There could be 500 blogs or more that they are a member of. In my brain, I would think that I would consider each user id’s meta and either don’t count them if any other roles appear in their capabilities. There is probably a better or easier way, I just have no clue.

I hope someone is up to the challenge!