A tank contains two immiscible liquids of densities
\[
6\rho
\quad \text{and} \quad
2\rho
\]
The higher density liquid is filled up to a height
\[
\frac L2
\]
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 position, the time period of small oscillations is
\[
\frac{2\pi}{n}\sqrt{\frac Lg}
\]
where \(g\) is the acceleration due to gravity. The value of \(n\) is _______.
