A Young's double-slit experiment is performed using monochromatic light of wavelength $\lambda$. The intensity of light at a point on the screen, where the path difference is $\lambda$, is K units. The intensity of light at a point where the path difference is $\frac{\lambda}{6}$ is given by $\frac{n K}{12}$, where $n$ is an integer. The value of $n$ is $\_\_\_\_$ .