Some proposals for replacing the Affordable Care Act $($Obamacare$)$ have relied on an existing mechanism called health flexible spending accounts $($FSA$$s$).$ At the beginning of the year, you decide how much money to put in an FSA. This money is deducted from your wages before taxes, thus reducing your tax payments. However, if you do not use all the money in the FSA by the end of the year, it reverts to your employer. A person who earns between $$85,526$ to $$163,300$ per year after deductions is in the $31\mathrm{.}65\%$ federal tax bracket $(7\mathrm{.}65\%$ for Social Security and Medicare, plus $24\%$ for income taxes$).$ Suppose such a person believes that their out$-$of$-$pocket health care expenses are equally like to be $$1000,$ $$1500,$ $$2000,$ $$2500,$ $$3000,$ $$3500,$ $$4000,$ or $$4500$ in the coming year. To maximize the expected benefit from their FSA, how much should they contribute to it$?$

Hint: to calculate G and L$,$ focus on the net after$-$tax effect on the person$$s bank account at the end of the year.