A mathlete has been tracking the percentage of problems he has gotten right so far this season.

Let $n$ be the number of problems given to him, and $m$ the number he has gotten correct.

Find the sum of all $0<q<0.85$ such that if at some point in the season $\frac{m}{n}<q$, and at some **later** point in the season $\frac{m}{n}>q$, then there will **always** be a third point in the season where $\frac{m}{n}=q.$

If you believe that no such $q$ exists, submit $-1$ as your answer.

**Clarification**: Although it is true that *any* rational $q$ may be obtained after the first two points, the problem requires that this rational $q$ *must* exist at some point in the season. In particular, it might be helpful to analyze points in the season *between* the two points satisfying the first two conditions.

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