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 \( a, b, c \) and \( d \) are integers. The value of \( \frac{b+c}{a+d} \) is _______.
