A $31$ year$-$old person plans to retire at $66$ and live until $94.$ During retirement, the person will take a growing annuity from the retirement account. The amount in the first year will be $$85,000$ with a $3\%$ growth rate.

The return on savings before retirement is $8\%,$ an after retirement is $6\%.$

Initial savings are zero, and the person does not want to leave a legacy at the time of death.

How much must the person save per year before retirement to achieve this goal?