The mentally ill homeless man accused of slashing two strangers and slapping a third within minutes of each other at a Queens subway station freely admitted his crimes when questioned by police, prosecutors said Saturday.

“Yeah, that’s me,” Tyquan Manassa told detectives when shown video images of the suspect on the Manhattan-bound E train platform in the Kew Gardens-Union Turnpike station on Wednesday afternoon.

Manassa, 27, also told investigators that he attacked the three strangers because he was “having a bad day,” a police source with knowledge of the case said.

He’s accused of slashing two men and slapping a third within a 15-minute explosion of fury on the train platform, Queens District Attorney Melinda Katz said.

“This random violence is every commuter’s worst nightmare,

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