In the figure shown, the npn transistor acts as a switch

For the inputV_in(t) as shown in the figure, the transistor switches between the cut-off and saturation regions of operation, when T is large. Assume collector-to-emitter voltage saturation V_CE(sat)=0.2V and base-to-emitter voltage V_BE=0.7V. The minimum value of the common-base current gain (α) of the transistor for the switching should be _____.