How to detect number of mouse/trackpad buttons?

I would like to automatically detect the number of buttons physically present on the mouse/trackpad device. My game will use different input logic if the user is using a mouse/trackpad with only one button (mac). Note I am not asking how to detect when right or middle button is pressed, I want to know if they physically exist.

Sure, one button devices have ways of simulating a right/secondary click, but they are awkward and since my game is also designed for a touch screen I already have a very streamlined way of using single button/touch input methods and I want to default to that option for those users with only one physical button.