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Other Benefit Plans (Narrative) (Details) - USD ($)
$ in Millions
12 Months Ended
Aug. 31, 2023
Aug. 31, 2022
Aug. 31, 2021
Deferred Compensation Arrangement with Individual, Postretirement Benefits [Line Items]      
Defined contribution plan, employer matching contribution, percent of match 50.00%    
Defined contribution plan, employer matching contribution, percent of employees' gross pay 6.60%    
Defined contribution plan, maximum annual contributions per employee percent 10.00%    
Discretionary non-elective contribution, percentage 5.00%    
Pension Plan, Defined Benefit      
Deferred Compensation Arrangement with Individual, Postretirement Benefits [Line Items]      
Defined contribution plan, cost recognized $ 4.6 $ 4.1 $ 3.9
International Pension Plans Defined Benefit      
Deferred Compensation Arrangement with Individual, Postretirement Benefits [Line Items]      
Defined contribution plan, cost recognized $ 2.1 $ 2.1 $ 1.9