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NEW YORK — A federal judge has cleared the way for investors who lost $1.2 billion to Wall Street swindler Bernard Madoff’s Ponzi scheme to receive $405 million in payouts.

New York Attorney General Eric Schneiderman said Monday that the judge rejected Madoff trustee Irving Picard’s challenge to the settlement his office arranged last year with J. Ezra Merkin.

Merkin ran a “feeder fund” that channeled money from four investment companies to Madoff.

Hundreds of investors had put their money into Ariel Fund, Gabriel Capital, Ascot Fund and Ascot Partners.

Merkin will also pay New York state $5 million for the expense of recovering the money.

Many eligible investors will be entitled to get more than 40 percent of their cash losses.

Madoff pleaded guilty in 2009 to fraud and is serving a 150-year prison sentence.