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Stock-Based Compensation - Schedule of Share-based Payment Award, Stock Options, Valuation Assumptions (Details) - $ / shares
12 Months Ended
Sep. 30, 2023
Sep. 30, 2022
Sep. 30, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected term 6 months 6 months 6 months
Expected dividend 0.00% 0.00% 0.00%
Tranche 1 [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Fair Value, Per Share $ 157.36    
Expected term 10 months 28 days    
Risk-free interest rate 4.66%    
Expected dividend 0.00%    
Tranche 1 [Member] | F5 [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected volatility 37.17%    
Tranche 1 [Member] | Index Members [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected volatility 35.56%    
Tranche 2 [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Fair Value, Per Share $ 173.68    
Expected term 1 year 10 months 28 days    
Risk-free interest rate 4.51%    
Expected dividend 0.00%    
Tranche 2 [Member] | F5 [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected volatility 31.84%    
Tranche 2 [Member] | Index Members [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected volatility 31.74%    
Tranche 3 [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Fair Value, Per Share $ 194.41    
Expected term 2 years 10 months 28 days    
Risk-free interest rate 4.44%    
Expected dividend 0.00%    
Tranche 3 [Member] | F5 [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected volatility 35.50%    
Tranche 3 [Member] | Index Members [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected volatility 40.59%