  We calculate analytically the current statistics for a short diffusive wire
between the normal reservoir and a short superconductor-normal
metal-superconductor (SNS) junction, at arbitrary applied voltages and
temperatures. The cumulant-generating function oscillates with the phase
difference $\phi$ across the junction, approaching the normal-state value at
$\phi=\pi$. At T=0 and at the applied voltage much smaller than the proximity
gap $\Delta_\phi$, the current noise $P_I$ doubles and the third current
cumulant $C_3$ is 4 times larger with respect to their values in the normal
state; at $eV \gg \Delta_\phi$ they acquire large excess components. At the gap
edge, $eV = \Delta_\phi$, the effective transferred charge defined through
$dP_I/dI$ and $dP_I/dV$ approaches $0e$ and $3e$, respectively, which makes
doubtful the interpretation of these quantities as physical elementary
transferred charge. At $T \neq 0$, $C_3$ shows a non-monotonous voltage
dependence with a dip near $eV = \Delta_\phi$.
