A ball of radius $r$ and density $\rho$ dropped through a viscous liquid of density $\sigma$ and viscosity $\eta$ attains its terminal velocity at time t , given by $t=A \rho^a r^b \eta^c \sigma^d$, where A is a constant and $\mathrm{a}, \mathrm{b}, \mathrm{c}$ and d are integers. The value of $\frac{b+c}{a+d}$ is $\_\_\_\_$ .