346 total teams (357 really but I read 11 are ineligible for one reason or another).
180 teams play in round 1. Afterward all teams left play.
256 teams play round 2
128 teams play round 3
64 teams play round 4
32 teams in round 5
Sweet Sixteen is round 6
Elite Eight is round 7
Final Four is round 8
Championship is round 9
I believe March Madness is 68 teams and 7 rounds right now, so this is only 2 extra rounds.