Three polaroid sheets $P_1$, $P_2$, and $P_3$ are kept parallel to each other such that the angle between the polarization axes of $P_1$ and $P_2$ is $45^\circ$, and that between $P_2$ and $P_3$ is $45^\circ$. If an unpolarized beam of light with an intensity of $128 \, \text{Wm}^{-2}$ is incident on $P_1$, what is the intensity of light coming out of $P_3$?