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Earnings Per Share (Details) - USD ($)
$ / shares in Units, $ in Thousands
 3 Months Ended
Nov. 27, 2021
Nov. 28, 2020
Earnings Per Share [Abstract]    
Net income $ 99,630 $ 57,423
Weighted average common shares outstanding (in shares) 33,322,000 33,609,000
Dilutive impact of stock compensation awards (in shares) 543,000 230,000
Dilutive impact of convertible notes (in shares) 513,000 0
Weighted average common shares outstanding, assuming dilution (in shares) 34,378,000 33,839,000
Anti-dilutive securities excluded from weighted average common shares outstanding, assuming dilution (in shares) 78,000 140,000
Basic earnings per common share (in dollars per share) $ 2.99 $ 1.71
Diluted earnings per common share (in dollars per share) $ 2.90 $ 1.70