Is there a auto arrange desktop icon hotkey?

Hello,

I know that you can right-click on desktop > view > check "auto arrange icons", but is there a shortcut/hotkey button that currently exists? I would like to just push a single button to quickly line them up for me, I do not want the auto arrange to be turned on always, just when the icons get a little bit out of control and needs a quick sort.

Is there a hotkey that does that already, or does anyone have a idea/solution where a shortcut with that functionality can be created?

I actually like to move all of my icons to the PUBLIC desktop folder and not the other way around as I use multiple logins to the same machine for various reasons. I use a batch file to do this.
Really you only need the one line: Call oIt %UserProfile% but I have the other two there for my convenience.

Code:

Set __COMPAT_LAYER=WinXP RunAdAdmin
Call :DoIt c:\Users\Glynr
Call :DoIt c:\Users\a
Call :DoIt %UserProfile%
pause

:DoIt
If Exist "%1\Desktop\*.*" Move /y "%1\Desktop\*.*" "%Public%\Desktop\"

:Quit
@Exit