Radial Resistivity Gradient

A solid, circular-cylindrical wire of length $L$ and radius $R$ has the following resistivity profile (where $r$ is the distance from the central axis):

$\large{\rho = e^{-r^2}}$

The total resistance between the two ends of the wire can be expressed as:

$\large{\frac{A \, L^B}{\pi \Big (e^{R^C} - 1 \Big )}}$

If $A,B,C$ are positive integers, what is $(A + B + C)$ ?