For more than 30 years, kids with a certain streak of genius have found a home at Illinois Mathematics and Science Academy in suburban Chicago. It’s the rarest of gems in the educational landscape: a public, affordable, boarding school. One of just a handful of such schools nationwide, Wired magazine dubbed it “ Hogwarts for Hackers .” But now, after the state’s two-year budget impasse , lawmakers are pondering a proposal that would welcome wizards from outside of Illinois — for a price.