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“We might want to believe that people are homeless because they’re drug addicts and they’re mentally ill and they’re criminals and all these other things and therefore it’s their own fault,” she said. “We can’t necessarily hold onto that for much longer. Because it’s a fantasy.”

She said she sees clients who work in local drugstores and restaurants but just can’t make ends meet, especially in a region where an omelet in some restaurants can cost as much as $30.

Forbes magazine this year named the village of Sagaponack in Southampton as the fourth-richest ZIP code in America, with a median home price of $4.1 million and a median income of $103,000, according to census figures.

Many of those who have vacation homes in the Hamptons, however, do not necessarily identify themselves as local residents for the purposes of the census and other data.

Suffolk County officials said this month that 20 Southampton families were being provided emergency shelter in one of its group homes, but noted the figures are constantly in flux. Suffolk listed 55 families in the town of Riverhead being housed in shelters.

“They’re working at Rite Aid and they’re working at Friendly’s; they’re not making enough money to put a roof over their head,’ Lutz said. ‘They’re making enough money to sort of buy some of the things that they need, so they come here so that they have a safe place to sleep.’

Maureen’s Haven operates on an annual budget of $340,000, much of which comes from private donations. Its offices feature several tables with computers where homeless clients can look for employment and available housing during the day.

Joann Piche, chairwoman of the Maureen’s Haven board of directors, said she understands it may be difficult for some to think of the Hamptons as a place where the homeless need help.

“The privet hedges, the beaches, the resort community, the gigantic homes that are used 12 weekends out of the year,” she said. “Every time I drive past one of these homes that for the most part are empty, I’m thinking, wow, how many people could we house in this place?”