The doubling time of {Escherichia coli is 30 minutes in a culture medium containing glucose and yeast extract. Phage T7 has a life cycle of 20 minutes and a burst size of 200 phage per infected {E. coli} cell. Phage absorption is instantaneous and occurs at 1 multiplicity of infection (MOI). Bacteria infected with multiple or single phage give the same burst. 5000 plaque forming units of T7 phage are added to a culture of \( 2 \times 10^7 \) {E. coli} cells. Assuming normal division, the {E. coli} culture will lyse completely by ........ full cycles of bacterial division. (Answer in integer)}