Cops are hunting a sex fiend wanted for raping and sexually attacking three women inside their Brooklyn high-rises.

The thug’s most recent assault was at 1:50 p.m. Friday, when he followed a 36-year-old woman into her apartment after waiting in the lobby of her Flatbush building near Flatbush and Bedford avenues.

He beat the woman’s face and raped her before fleeing out a bedroom window and down a fire escape.

The same violent perv is believed to have attacked a 32-year-old woman in May and a 28-year-old woman two years ago.