$2 \mathrm{MnO}_4^{-}+\mathrm{bI}^{-}+\mathrm{cH}_2 \mathrm{O} \rightarrow x \mathrm{I}_2+y \mathrm{MnO}_2+z \overline{\mathrm{O}} \mathrm{H}$

If the above equation is balanced with integer coefficients, the value of $z$ is ________.