U-360 Wiring Question

[gamepimp]

I am wiring all of my buttons up directly to the U-360 instead of using a keyboard encoder like the IPAC. The connector on the joystick has a common ground and inputs for 8 buttons. Each player on my CP has 6 buttons and both a coin and start button. So I have 8 buttons total which should be perfect. I also have a coin door in my cabinet that I want to be functional. So I was going to just take the "normally open" input from each microswitch in the coin door and wire it to the corresponding coin button on the CP. Not too complicated, right? The only thing I'm not sure of is the ground for the coin door switches. Can I just link them all together and wire to a single U-360's ground? Or do I need to run a ground wire from each coin door switch to the ground wire of the corresponding U-360? (thus having four separate ground wires coming from the coin door)