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Stock-Based Compensation - Schedule of Share-based Payment Award, Stock Options, Valuation Assumptions (Details) - $ / shares
12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
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 $ 283.35    
Expected term 10 months 28 days    
Risk-free interest rate 0.13%    
Expected dividend 0.00%    
Tranche 1 [Member] | F5 [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected volatility 26.21%    
Tranche 1 [Member] | Index Members [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected volatility 27.27%    
Tranche 2 [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Fair Value, Per Share $ 302.53    
Expected term 1 year 10 months 28 days    
Risk-free interest rate 0.47%    
Expected dividend 0.00%    
Tranche 2 [Member] | F5 [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected volatility 35.13%    
Tranche 2 [Member] | Index Members [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected volatility 42.87%    
Tranche 3 [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Fair Value, Per Share $ 308.76    
Expected term 2 years 10 months 28 days    
Risk-free interest rate 0.76%    
Expected dividend 0.00%    
Tranche 3 [Member] | F5 [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected volatility 32.54%    
Tranche 3 [Member] | Index Members [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected volatility 38.24%