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A set of 1985 points is distributed around the circumference of a circle and each of the points is marked with 1 or -1. A point is called “good” if the partial sums that can be formed by starting at that point and proceeding around the circle for any distance in either direction are all strictly positive. Show that if the number of points marked with -1 is less than 662, there must be at least one good point.

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