A person without current savings plans to retire in $36$ years and receive a growing annuity starting with $$99,000$ in the first year and growing $2\%$ each year thereafter. The plan is for a $22-$year retirement period and leaving a legacy of $$300,000$ at the end. The pre$-$retirement return is $9\%,$ and the return during retirement will be $7\%.$

Prior to retirement, how much must the person begin saving per year to achieve the retirement goal?