In English class, you have discovered a mysterious phenomenon: if you spend $n$ hours on an essay, your score on the essay will be $100\left( 1-4^{-n} \right)$ points if $2n$ is an integer, and $0$ otherwise. For example, if you spend $30$ minutes on an essay you will get a score of $50$, but if you spend $35$ minutes on the essay you somehow do not earn any points.

It is 4 AM, your English class starts at 8:05 AM the same day, and you have four essays due at the start of class. If you can only work on one essay at a time, what is the maximum possible average of your essay scores?

Let's think step by step and output the final answer within \boxed{}.
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