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Stock-Based Compensation - Assumptions Used to Value Stock Options (Details)
6 Months Ended
Mar. 31, 2023
$ / shares
Share-Based Payment Arrangement [Abstract]  
Dividend yield 0.00%
Risk-free interest rate 3.69%
Expected volatility 86.40%
Expected life (in years) 6 years 3 months
Weighted average grant date fair value per share of options granted $ 24.80