**m** each are moving about the center of mass of the system such that they are always on the vertices of a regular hexagon of the side-length having length **a** each.Their common time period can be determined in the form of
$w \pi \times \sqrt{ \frac {x \sqrt{3} a^{3} }{Gm(y+z \sqrt{3} ) } }$ where w,x,y,z are positive integers.Find **w+x+y+z**.