The figure shows four identical conducting spheres that are actually well separated from one another. Sphere W $($with an initial charge of zero$)$ is touched to sphere A and then they are separated. Next, sphere W is touched to sphere B $($with an initial charge of $-34$e$)$ and then they are separated. Finally, sphere W is touched to sphere C $($with an initial charge of $48$e$),$ and then they are separated. The final charge on sphere W is $14$e$.$ What multiple of e gives the initial charge on sphere A$?$

Four identical spheres labeled A$,$ B$,$ C$,$ and W$.$ The spheres are well separated. Sphere A is in the top left corner. Sphere B is to the right of A and sphere C is to the right of B$.$ Sphere W is directly below A$.$

The figure shows four identical conducting spheres that are actually well separated from one another. Sphere $W($with an initial charge of zero$)$ is touched to sphere A and then they are separated. Next, sphere $W$ is touched to sphere $B($with an initial charge of $-34e)$ and then they are separated. Finally, sphere $W$ is touched to sphere $C($with an initial charge of $48e),$ and then they are separated. The final charge on sphere $W$ is $14e.$ What multiple of e gives the initial charge on sphere $A?$