Haley has an annual salary of $$1,000,000$ in $2020,2021,$ and $2022.$ She is thinking about retiring at the beginning of $2023$ after working for XYZ Corporation and participating in XYZ Corporation's defined benefit plan. If XYZ Corporation's defined benefit plan pays employees $3$ percent for every year of service for the average of their three highest years of compensation, what is the minimum number of years of service that would maximize Haley's benefit if she were to retire at the beginning of $2023?$ Assuming she worked the minimum number of years to receive the maximum benefit, what would her annual defined benefit plan payment be in retirement?