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By Scott Malone and Jill Serjeant BOSTON/NEW YORK (Reuters) - A blizzard swept across the northeastern United States, dropping more than a foot (30 cm) of snow but falling short of more dire predictions that sent workers and students home, halted thousands of flights and prompted New York officials to ban cars from roads and shut down subway trains. As day broke on Tuesday, the leaders of New York City, New York state and New Jersey began lifting travel bans imposed the night before, when forecasters warned of a potentially "historic" blizzard that could dump as much as 3 feet (90 cm) of snow and paralyze the East Coast. The National Weather Service lifted its blizzard warning for New York City, downgrading it to a winter storm warning, but cautioned that snow could fall off and on until midnight. "We thought we were going to get something a lot bigger," New York City Mayor Bill de Blasio told CNN.