What is the minimum amount of money it takes to open a Swiss bank account, and can you open from USA?

I have always prided myself on being a shadowy and mysterious person, so this would be the ultimate accoutrement to reinforce my personality. I just want to open a Swiss bank account, but I have no time or resources to open one in person, I am sure it should be easy enough to open one from the US and wire over some money to open it, but what is the minimum amount needed to open an account at your typical Swiss bank? I would also like to know if a numbered account costs more to open up or requires a higher balance or is just simply a different type of account.