In the figure shown, the $npn$ transistor acts as a switch.
For the input $V_{in}(t)$ 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 at saturation $V_{CE(sat)}=0.2V$ and base-to-emitter voltage $V_{BE}=0.7V$.The minimum value of the common-base current gain $(\alpha)$ of the transistor for the switching should be __________.