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Income Per Share - Narrative (Details) - shares
3 Months Ended 9 Months Ended
May 28, 2022
May 29, 2021
May 28, 2022
May 29, 2021
Earnings Per Share [Abstract]        
Anti-dilutive securities excluded from calculation of diluted earnings per share (in shares) 43,246 2,189 36,373 1,770