I always check one bag and carry on a smaller carry on that typically fits under the seat, plus a purse. I am presenting a poster session and need to carry on a 36" tube-shaped case carrying the poster. Will this be counted as a 3rd carry on? I really need all three of these items and don't want to check any of them. I had thought that I could stick the poster tube into my carry on and leave it sticking out, but this still looks pretty big. My purse is too big to put into my carry on. Help!