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Revenue Recognition - Contract Assets and Liabilities and Remaining Performance Obligations (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended 12 Months Ended
Feb. 28, 2022
Aug. 31, 2021
Feb. 28, 2021
Aug. 31, 2020
Feb. 28, 2022
Feb. 28, 2021
May 31, 2021
Contract Assets and Liabilities              
Contract assets - current $ 68.8       $ 68.8   $ 71.9
Contract assets - non-current 22.4       22.4   21.6
Contract liabilities:              
Deferred revenue - current (26.8)       (26.8)   (25.9)
Deferred revenue on long-term contracts (8.7)       (8.7)   (5.4)
Net contract assets (liabilities) 55.7       55.7   62.2
Change in contract assets - current         (3.1)    
Change in contract assets - Noncurrent         0.8    
Change in contract liabilities - current         (0.9)    
Change in contract liabilities - non-current         (3.3)    
Change in net contract assets         (6.5)    
Charge related to termination of PBH customer contract     $ 3.5 $ 2.2      
Change in contract assets         (2.9) $ 16.8  
PBH forward loss reserve 1.5       1.5    
Change in Contract with Customer, Liability              
Deferred revenue at beginning of period (42.7) $ (31.3) (48.4) $ (99.2) (31.3) (99.2) (99.2)
Revenue deferred (81.9)   (61.7)   (204.0) (184.7)  
Revenue recognized 82.4   72.4   187.4 248.5  
Other 6.7   (0.6)   12.4 (2.9)  
Deferred revenue at end of period (35.5)   $ (38.3)   (35.5) $ (38.3) (31.3)
Remaining Performance Obligations              
Remaining performance obligation $ 825.0       825.0    
Accrued liabilities              
Contract liabilities:              
PBH forward loss reserve         $ 0.9    
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]: 2021-09-01              
Remaining Performance Obligations              
Remaining performance obligation (as a percent) 40.00%       40.00%    
Expected timing of satisfaction of remaining performance obligation 12 months       12 months    
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]: 2022-09-01              
Remaining Performance Obligations              
Remaining performance obligation (as a percent) 40.00%       40.00%    
Expected timing of satisfaction of remaining performance obligation 3 years       3 years    
PBH contracts              
Contract liabilities:              
Charge related to early termination of PBH customer contract   5.2          
Change in contract assets   1.0          
PBH forward loss reserve $ 4.6       $ 4.6    
PBH forward loss reserve   4.2          
Contract Charges on non-achievement of minimum volume guarantees             $ 4.5
Charge to increase obligation reflecting revised estimated shortfall on minimum volume guarantee   $ 1.7          
PBH contracts | Accrued liabilities              
Contract liabilities:              
PBH forward loss reserve 1.5       1.5    
PBH contracts | Other liabilities              
Contract liabilities:              
PBH forward loss reserve $ 3.1       $ 3.1