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Let \(S\) be the set of positive integers \(k\) such that the two parabolas$$y=x^2-k~~\text{and}~~x=2(y-20)^2-k$$intersect in four distinct points, and these four points lie on a circle with radius at most \(21\). Find the sum of the least element of \(S\) and the greatest element of \(S\).