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Income Taxes and Other Taxes (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
Feb. 28, 2022
Aug. 31, 2021
Feb. 28, 2021
Feb. 28, 2022
Feb. 28, 2021
Operating Loss Carryforwards [Line Items]          
Current liability $ 3.8     $ 3.8  
Effective income tax rate (percentage) 23.70%   36.40% 19.70% 29.00%
Tax Years 2015 to 2020          
Operating Loss Carryforwards [Line Items]          
Income taxes receivable $ 20.0     $ 20.0  
Employee Retention Credits          
Operating Loss Carryforwards [Line Items]          
Income taxes receivable $ 11.9     $ 11.9  
Carry Back of Net Operating Losses          
Operating Loss Carryforwards [Line Items]          
Proceeds from Income Tax Refunds   $ 63.1