Let $X$ and $Y$ be continuous random variables with probability density functions $P_X(x)$ and $P_Y(y)$, respectively. Further, let $Y=X^2$ and $P_X(x)=\left\{\begin{array}{cc}1, & x \in(0,1] \\ 0, & \text { otherwise }\end{array}\right.$.

Let $a_R$ be the unit radial vector in the spherical co-ordinate system. For which of the following value(s) of $n$, the divergence of the radial vector field $f(R)=a_R \frac{1}{R^n}$ is independent of $R$ ?