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Stock-Based Compensation Plans - Narrative (Details) - USD ($) $ in Millions	12 Months Ended
	Aug. 26, 2023	Aug. 27, 2022	Aug. 28, 2021	Dec. 11, 2018
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Accrued compensation	$ 35.9	$ 71.6
Unrecognized compensation expense related to stock options	$ 1.6
Stock options
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Outstanding options term	10 years
Vesting period	3 years
Unrecognized compensation expense, period of recognition	10 months 24 days
Performance-based
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period	3 years
Unrecognized compensation expense	$ 4.9
Unrecognized compensation expense, period of recognition	1 year
Total fair value of awards vested	$ 7.6	5.8	$ 1.4
Time-based
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Unrecognized compensation expense	$ 10.1
Unrecognized compensation expense, period of recognition	10 months 24 days
Total fair value of awards vested	$ 8.8	$ 8.0	$ 5.2
Time-based \| Director
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period	1 year
ESPP
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of shares authorized (in shares)	250,000
Discount market price percentage	15.00%
Shares purchased through the ESPP (in shares)	29,000	42,000
Accrued compensation	$ 0.5	$ 0.4
Shares remain available for future issuance (in shares)	34,000
Incentive Compensation Plan 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of shares authorized (in shares)				4,100,000