NYPD detectives spent Tuesday trying to piece together the life, travels and finances of Ismaaiyl Brinsley, the man who killed two NYPD officers Saturday in Brooklyn before taking his own life.

Brinsley, 28, described as a suicidal man who for weeks spewed angry social media postings against the government and police, shot and killed officers Wenjian Liu and Rafael Ramos in their police vehicle in Bedford-Stuyvesant.

Liu, 32, was covering the shift of another officer in a special anti-crime assignment at about 2:47 p.m. when he was slain with Ramos, 40, a law enforcement official said.

Investigators said ShotSpotter, an acoustical system being tested in New York to quickly detect and locate shootings, picked up the sounds of the four shots that killed the officers and pinpointed their location.

After shooting the officers, Brinsley fled to a nearby subway station with police in pursuit. He then fatally shot himself. Cops found a Taurus 9-mm pistol that federal officials traced to a legal 1996 purchase at a pawnshop in the Atlanta area. The gun was sold again legitimately in 1998, and officials are trying to find out how Brinsley got it.

Officials with the NYPD and federal Bureau of Alcohol, Tobacco, Firearms and Explosives couldn't be reached for comment Tuesday about progress on the gun trace or other elements of the investigation.

Investigators are asking anyone with information on the final leg of his homicidal trip -- 12:07 p.m. until the moment he ambushed the two officers -- to contact them.

It remains a mystery to detectives how Brinsley acquired the means to travel around the South and to Baltimore County, Maryland, before arriving in New York City. His mother said he was mentally troubled, and Police Commissioner William Bratton said the shooter had no apparent stable job.

Bratton said Monday that detectives are trying to reconstruct Brinsley's financial history and bank card uses.

After shooting and wounding his girlfriend in Baltimore County earlier Saturday, Brinsley took a bus to Manhattan and entered the city through the Lincoln Tunnel, according to a trace of his cellphone records, investigators said.

Brinsley apparently took the subway to the Atlantic Center mall, where surveillance cameras captured him walking around with a foam food container in a bag, and apparently talking on a cellphone that he then ditched. Detectives recovered the phone and have been analyzing its contents.

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