International applicants dropping by over 25 percent at Illinois’s flagship university and several dozen international students withdrawing from the University of Maryland, Baltimore, just weeks before the start of the semester.

Those are just two of the ways colleges said, in court filings, that new limits on how long international students can stay in the U.S. are already having an effect, even before the rule officially kicks in next month. Under the rule, international students can stay for only four years before seeking an extension. Previously, they could remain in the country until their studies were completed.

A lawsuit filed last week is aiming to stop the controversial rule before the Sept. 15 start date; the plaintiffs argue that the Department of Homeland Security did not adequately consider the impacts of the rule before finalizing it.

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