High-tech DNA testing has solved two gruesome crimes that have baffled investigators for nearly three decades — the murder and rape of two elderly Long Island psychiatric patients, prosecutors said.

Steven Briecke, a career criminal whose rap sheet includes the sex assault of a teenager and a string of public lewdness busts, was identified as the monster who murdered 69-year-old Ann Lustig in 1997 and raped an 82-year-old psychiatric patient in 1996, the Suffolk County District Attorney’s office said .

Unfortunately for the victims’ families, Briecke died 12 years ago.

“Resolving long-overdue crimes that have haunted victims loved ones and our community for far too long is why we established the Cold Cast Task Force,” Suffolk DA Ray Tierney said in a statement Monday.

“Thanks to the

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