A trader creates a long butterfly spread from options with strike prices X$,$ Y$,$ and Z$,$ where X $<$ Y $<$ Z$,$ and Y is exactly midway between X and Z$.$ A total of $400$ options are traded.$$ The difference between X and Y is $$12.$ The difference in the prices of the options with strike prices of X and Y is $$5\mathrm{.}2.$ The difference in the prices of the options with strike prices of Y and Z is $$6\mathrm{.}91.$ What is the maximum net loss $($after the cost of the options is taken into account$)?$ Please give your answer to the nearest dollar. answer is $171$