The maximum frequency for reflection of sky waves from a certain layer of the ionosphere is found to be f_max = 9(N_max)^1/2, where N_max is the maximum electron density at that layer of the ionosphere. On a certain day it is observed that signals of frequencies higher than 5MHz are not received by reflection from the F₁ layer of the ionosphere while signals of frequencies higher than 8MHz are not received by reflection from the F₂ layer of the ionosphere. Estimate the maximum electron densities of the F₁ and F₂ layers on that day.