Diar Corporation purchased a patent for $$405,000$ on September $1,2019.$ It had a useful life of $10$ years. On January $1,2021,$ Diar spent $$149,000$ to successfully defend the patent in a lawsuit. Diar feels that as of that date, the remaining useful life is $5$ years. What amount should be reported for patent amortization expense for $2021?$

a$.$ $$70,200.$

b$.$ $$100,000.$

c$.$ $$84,600.$

d$.$ $$90,000.$