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Stock-Based Compensation Plans - Narrative (Details) - USD ($) $ in Millions		12 Months Ended
	Dec. 14, 2023	Aug. 31, 2024	Aug. 26, 2023	Aug. 27, 2022
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Accrued compensation		$ 35.9	$ 35.9
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		9 months 18 days
Performance-based
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period		3 years
Unrecognized compensation expense		$ 5.0
Unrecognized compensation expense, period of recognition		1 year 2 months 12 days
Total fair value of awards vested		$ 4.5	7.6	$ 5.8
Time-based
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Unrecognized compensation expense		$ 10.0
Unrecognized compensation expense, period of recognition		9 months 18 days
Total fair value of awards vested		$ 8.4	$ 8.8	$ 8.0
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)		550,000
Shares remain available for future issuance (in shares)		353,000
Discount market price percentage		15.00%
Shares purchased through the ESPP (in shares)		47,000	29,000
Accrued compensation		$ 0.5	$ 0.5
Incentive Compensation Plan 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of shares authorized (in shares)	2,400,000
Counted against share reserve (in shares)	2
Incentive Compensation Plan 2014
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares remain available for future issuance (in shares)		3,800,000