In E. coli, the ability to utilize lactose as a carbon source requires the presence of the enzymes b-galactosidase and b-galactoside permease. These enzymes are encoded by two closely linked genes, lacZ and lacY, respectively. Another gene, proC, controls, in part, the ability of E. coli cells to synthesize the amino acid proline. The alleles strr and strs, respectively, control resistance and sensitivity to streptomycin. Hfr H is known to transfer the two lac genes, proC, and str, in that order, during conjugation. A cross was made between Hfr H of genotype lacZ⁻ lacY⁺ proC⁺ strs and an F⁻ strain of genotype lacZ⁺ lacY⁻ proC⁻ strr. After about 2 hours, the mixture was diluted and plated out on medium containing streptomycin but no proline. When the resulting proC⁺ strr recombinant colonies were checked for their ability to grow on medium containing lactose as the sole carbon source, very few of them were capable of fermenting lactose. When the reciprocal cross (Hfr H lacZ⁺ lacY⁻ proC⁺ strs X F⁻ lacZ⁻ lacY⁺ proC⁻ strr) was done, many of the proC⁺ strr recombinants were able to grow on medium containing lactose as the sole carbon source. What is the order of the lacZ and lacY genes relative to proC?