Stock-Based Compensation Plans - Share Awards Activity (Details)	12 Months Ended
	Aug. 27, 2022 $ / shares shares
Time-based
Shares
Beginning balance (in shares) | shares	330,819
Granted (in shares) | shares	147,236
Vested (in shares) | shares	(111,832)
Forfeited/canceled (in shares) | shares	(37,385)
Ending balance (in shares) | shares	328,838
Weighted Average Fair Value
Beginning balance (in dollars per share) | $ / shares	$ 44.35
Granted (in dollars per share) | $ / shares	73.64
Vested (in dollars per share) | $ / shares	45.53
Forfeited/canceled (in dollars per share) | $ / shares	55.05
Ending balance (in dollars per share) | $ / shares	$ 55.85
Performance-based
Shares
Beginning balance (in shares) | shares	227,751
Granted (in shares) | shares	88,557
Vested (in shares) | shares	(76,413)
Forfeited/canceled (in shares) | shares	(41,689)
Ending balance (in shares) | shares	198,206
Weighted Average Fair Value
Beginning balance (in dollars per share) | $ / shares	$ 45.81
Granted (in dollars per share) | $ / shares	68.59
Vested (in dollars per share) | $ / shares	40.46
Forfeited/canceled (in dollars per share) | $ / shares	43.93
Ending balance (in dollars per share) | $ / shares	$ 58.45