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SCHOOL FLAP OVER HOT TOT SPOTS

They already won a high-stakes lottery that earned their kids coveted pre-kindergarten slots in school this year.

But now parents at some popular lower Manhattan public schools are livid after learning that their children must win a second long-shot lottery in order to stay in the same school come September.

“It’s very distressing to me and my family,” said Erin Sun, whose 4-year-old daughter, Violet, is at risk of being bounced from the national blue-ribbon school Shuang Wen in Chinatown.

“I just find it hard to believe that anyone who cares about children would make a 4-year-old leave their friends, teachers and a comfortable environment simply for an arbitrary reason.”

Kids at three sought-after schools in District 1 – the dual-language Shuang Wen, the Neighborhood School and Earth School – have the greatest chance of being booted for the upcoming year.

That’s because unlike the other 31 school districts in the city, District 1 doesn’t align schools to particular neighborhoods – something that basically guarantees kids who live near a school a kindergarten spot there.

The Department of Education for years has been threatening to enforce a policy that opens kindergarten slots at District 1 schools to anyone in the district – with no preference at a particular school for those already enrolled.

But this is the first time in recent memory that the policy is being enforced, according to parents.

“I don’t know what I’m going to do if he doesn’t get in [again],” Harvey Epstein, 41, said of his son, Joshua Eliot, who attends pre-kindergarten at the Neighborhood School in the East Village. “We really think this policy has to change.”

Department spokesman Andy Jacob said that officials made it clear to parents last year that the policy would be enforced this year.

The change is meant to give kids who aren’t enrolled in pre-kindergarten an equal shot at a desirable kindergarten seat.

“From our point of view, it’s the fairest way to do it,” Jacob said.

yoav.gonen@nypost.com