The reason I made you record the exam was that if there was something I do not understand from your solutions, I could go back and listen to your discussions. I am very sorry that some of you felt the need to ask for permission to go to bathroom during the exam and were very apologetic for that. I should have made clear that this is allowed. You can not do mathematics if you are trying to not think about going to bathroom. So, let me just say this here: You can go to bathroom during the final exam.