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Retirement Plans - Defined Contribution Retirement Plans (Details) - USD ($)
$ in Millions
12 Months Ended
Sep. 30, 2022
Sep. 30, 2021
Sep. 30, 2020
Defined Contribution Plan Disclosure [Line Items]      
Defined contribution plan, employer discretionary contribution amount $ 16.9 $ 15.2 $ 10.1
United States | 401k Plan      
Defined Contribution Plan Disclosure [Line Items]      
Defined contribution plan, employer matching contribution, percent of employees' gross pay 62.50%    
Defined contribution plan, employers matching contribution, annual vesting percentage 8.00%    
Defined contribution plan, employers matching contribution, annual vesting percentage, two to three years 33.00%    
Defined contribution plan, employers matching contribution, annual vesting percentage, three to four years 66.00%    
Defined contribution plan, employers matching contribution, annual vesting percentage, all years 100.00%    
United Kingdom      
Defined Contribution Plan Disclosure [Line Items]      
Defined contribution plan, employers matching contribution, annual vesting percentage 100.00%    
Minimum | United States | 401k Plan      
Defined Contribution Plan Disclosure [Line Items]      
Defined contribution plan, annual contributions per employee, percent 1.00%    
Maximum | United States | 401k Plan      
Defined Contribution Plan Disclosure [Line Items]      
Defined contribution plan, annual contributions per employee, percent 80.00%    
Maximum | United Kingdom      
Defined Contribution Plan Disclosure [Line Items]      
Defined contribution plan, employer matching contribution, percent of employees' gross pay 10.00%