S3 only (don't also upload to WordPress' server)

I only want the uploads to go to S3 because of limited storage space on my server's hard drive.

I don't just want a CDN like MaxCDN because all the files are still on my server; they're just cached with MaxCDN.

I actually want my entire Media Library or whatever other files to be in S3 and not also on my server.

So all references to http://www.example.com/wp-content/uploads/file.jpg should instead be s3.example.com/... or whatever.

How can this be done?

Thank you.