A thin uniform rod of length $$L$$ and certain mass is kept on a frictionless horizontal table with a massless string of length $$L$$ fixed to one end (top view is shown in the figure). The other end of the string is pivoted to a point $$O$$. If a horizontal impulse $$P$$ is imparted to the rod at a distance $$x = L/n$$ from the mid-point of the rod (see figure), then the rod and string revolve together around the point $$O$$, with the rod remaining aligned with the string. In such a case, the value of $$n$$ is ______.