CHICAGO (Reuters) - A group of Chicago female public defenders has sued the operator of one of the nation’s largest jails and their employer in federal court over sexual harassment by inmates, including masturbation often directed at them.

FILE PHOTO: A Cook County Sheriff's police car patrols the exterior of the Cook County Jail in Chicago, Illinois, U.S. on January 12, 2016. REUTERS/Jim Young/File Photo

The lawsuit, filed Wednesday in U.S. District Court in Chicago by six Cook County public defenders, alleges that more than 200 female defenders and law clerks since 2015 have endured “heinous sexual misconduct” by male inmates in the jail and courtroom holding cells.

The Cook County jail inmates “have repeatedly exposed their penises, masturbated, and engaged in other acts of sex-based aggression, verbal threats and harassment, and on an almost daily basis,” threatening the women, the lawsuit said.

The Cook County Public Defender and the Cook County Sheriff, which operates the jail, failed to protect the women, according to suit, which seeks remedial action and damages.

More than half of the 419 public defenders for Cook County, which includes Chicago, are women.

“There have been weeks when (assistant public defender Saran Crayton) experienced a detainee exposure or masturbation incident every day,” the suit said of one of the plaintiffs.

Cara Smith, chief policy officer for Sheriff Tom Dart, said Thursday that the problem has bedeviled them for years and solutions have proved elusive.

Lester Finkle, chief of staff for the public defender’s office, said his office was working on a solution.

“However, the Public Defender cannot support legislation or measures that significantly increase penalties for detainees who engage in this behavior or that subject detainees to inhumane practices,” Finkle said in a statement.

The sheriff’s office tried adding deputies, which was costly, and also using special jumpsuits to restrict access to inmates genitals, but that was discontinued when inmates burned the jumpsuits in microwave ovens, the suit said.

At one point, the sheriff’s office instituted a program rewarding serial masturbators with pizza if they went 30 days without another incident, the suit said, but that only led more to masturbate. The sheriff’s office has suggested video court hearings to reduce exposure, Smith said.

More than 200 detainees have been charged with indecent exposure since January, but few facing murder or rape charges seem to care about a misdemeanor charge, Smith said.

“This kind of behavior unfortunately is prevalent in correctional settings, whether in state prison or jails - and it’s not just here in Illinois,” she said.

The jail houses more than 6,440 inmates, making it one of the largest in the nation, jail officials said.