Stock-Based Compensation Plans - Share Awards Activity (Details)	12 Months Ended
	Aug. 26, 2023 $ / shares shares
Time-based
Shares
Beginning balance (in shares) | shares	328,838
Granted (in shares) | shares	221,777
Vested (in shares) | shares	(153,806)
Forfeited/canceled (in shares) | shares	(14,048)
Ending balance (in shares) | shares	382,761
Weighted Average Fair Value
Beginning balance (in dollars per share) | $ / shares	$ 55.85
Granted (in dollars per share) | $ / shares	56.13
Vested (in dollars per share) | $ / shares	53.49
Forfeited/canceled (in dollars per share) | $ / shares	59.88
Ending balance (in dollars per share) | $ / shares	$ 56.81
Performance-based
Shares
Beginning balance (in shares) | shares	198,206
Granted (in shares) | shares	149,962
Vested (in shares) | shares	(135,520)
Forfeited/canceled (in shares) | shares	0
Ending balance (in shares) | shares	212,648
Weighted Average Fair Value
Beginning balance (in dollars per share) | $ / shares	$ 58.45
Granted (in dollars per share) | $ / shares	53.11
Vested (in dollars per share) | $ / shares	49.18
Forfeited/canceled (in dollars per share) | $ / shares	0
Ending balance (in dollars per share) | $ / shares	$ 60.59