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Stock-Based Compensation - Schedule of Share-based Payment Award, Stock Options, Valuation Assumptions (Details) - $ / shares
12 Months Ended
Sep. 30, 2024
Sep. 30, 2023
Sep. 30, 2022
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 $ 192.58    
Expected term 10 months 28 days    
Risk-free interest rate 5.32%    
Expected dividend 0.00%    
Tranche 1 [Member] | F5 [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected volatility 22.60%    
Tranche 1 [Member] | Index Members [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected volatility 27.66%    
Tranche 2 [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Fair Value, Per Share $ 203.37    
Expected term 1 year 10 months 28 days    
Risk-free interest rate 4.93%    
Expected dividend 0.00%    
Tranche 2 [Member] | F5 [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected volatility 31.25%    
Tranche 2 [Member] | Index Members [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected volatility 32.35%    
Tranche 3 [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Fair Value, Per Share $ 210.37    
Expected term 2 years 10 months 28 days    
Risk-free interest rate 4.72%    
Expected dividend 0.00%    
Tranche 3 [Member] | F5 [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected volatility 29.55%    
Tranche 3 [Member] | Index Members [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected volatility 30.88%