A sol contains $0.50\mathrm{M}$ of an ionic impurity. It is dialysed repeatedly. In each cycle the sol volume $V$ is brought to equilibrium with a fresh pure-water volume of $4V$ and the water is then discarded. What is the minimum number of cycles needed to bring the impurity concentration below $1.0\mathrm{mM}$? (Use $\log 2=0.301$ and $\log 5=0.699$.)

Numerical answer type, answer in cycles, tolerance 0.1.