Linda purchased a cottage in $1984$ for $$62,000$; on February $22,1994,$ it was valued at $$126,000.$ On her $1994$ tax return, Linda elected to make use of her remaining lifetime capital gains exemption in the amount of $$55,000$ by recognizing a notional disposition on the cottage$.$ If Linda sells the cottage today for $$670,000,$ how much of a capital gain will Linda realize?

a$)$ $$553,000$

b$)$ $$615,000$

c$)$ $$526,500$

d$)$ $$608,000$