Simple Harmonic Motion

A tank contains two immiscible liquids of densities $6\rho$ and $2\rho$. The higher density liquid is filled up to a height $L/2$ from the bottom. A thin rod of density $\rho$ and length $L$ is fully immersed and hinged at the bottom so that it can oscillate freely, as shown in the figure. If the rod is slightly disturbed from its equilibrium, the time period of small oscillations is \(\frac{2\pi}{n}\sqrt{\frac{L}{g}},\) where $g$ is the acceleration due to gravity. The value of $n$ is: