A homeless maniac went on a wild punching spree in Midtown Tuesday — randomly attacking three men, including one in the lobby of the fancy One Vanderbilt skyscraper, cops and sources said.

Jordan Velez, 29, first allegedly punched an unsuspecting 61-year-old man in the face on Madison Avenue near East 40th Street around 12:15 p.m., according to authorities and sources.

He went on to randomly strike a 34-year-old man just outside the 73-story skyscraper at the corner of East 42nd Street and Vanderbilt Avenue – before storming inside the lobby of the iconic building and dealing another blow to a 23-year-old man, the sources said.

Jordan Velez, 29, allegedly punched three victims at random — the younger two either just outside or in the lobby of the One Vanderbilt skyscraper, cops and sour

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