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Earnings Per Share - Narrative (Details) - shares
3 Months Ended
Nov. 30, 2021
Nov. 30, 2020
Stock options    
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]    
Antidilutive securities excluded from computation of earnings per share (in shares) 298,900 1,750
Performance-based awards    
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]    
Antidilutive securities excluded from computation of earnings per share (in shares) 97,511 72,090