The Rhône flows into the sea at the Mediterranean Sea. Let's give that a score of 1. The Saône flows into the Rhône, so that's a score of 2. The Doubs flows into it, giving a score of 3. Using only named waterways, I wonder what's the highest scoring thing?

(This is sorta related to Strahler number maybe. I could probably figure this out from #OpenStreetMap)