Sara is filing as head of household and has $2023$ taxable income of $$66,000,$ which includes $$3,000$ of net long$-$tem capital gain. The net long$-$term capital gain is made up of $$1,00025\%$ gain and $$2,0000\%/15\%/20\%$ gain. What is the tax on her taxable income using the alternative tax method? Note: Use the tax rate schedule rather than the tax table.

a$.$ $$8,081.$

b$.$ $$8,221.$

c$.$ $$8,311.$

d$.$ $$0$