I am trying to create a circuit but I don't know exactly which switch design or logic chip I would use to accomplish my goal.

Here's the scenario: I have 6 pins, let's call them A, B and C and 1, 2 and 3. I want to use a pushbutton switch to move through 3 different ways of connecting these pins.

Position 1: Pin A is connected to Pin 1, Pin B is connected to Pin 2, Pin C is connected to Pin 3 Position 2: Pin A is connected to Pin 2, Pin B is connected to Pin 3, Pin C is connected to Pin 1 Position 2: Pin A is connected to Pin 3, Pin B is connected to Pin 1, Pin C is connected to Pin 2

What is the simplest way of accomplishing this circuit using a pushbutton as the control interface?

Attached is a diagram in case that helps.

Thanks so much for any feedback!