2 MnO_4^-+ bI^-+ cH_2 O → x I_2+y MnO_2+z Ō H If the above equation is balanced with integer coefficients, the value of z is ____.

$$2 \mathrm{MnO}_4^{-}+\mathrm{bI}^{-}+\mathrm{cH}_2 \mathrm{O} \rightarrow x \mathrm{I}_2+y \mathrm{MnO}_2+z \overline{\mathrm{O}} \mathrm{H} $$ If the above equation is balanced with integer coefficients, the value of $\displaystyle z$ is $\displaystyle \_\_\_\_$.