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Share-Based Compensation - Narrative (Details) - USD ($)	12 Months Ended
	Aug. 29, 2026	Aug. 30, 2025	Aug. 31, 2024	Oct. 31, 2023
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share based payment arrangement, expense	$ 0
Stock Appreciation Rights (SARs)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percentage vested after each anniversary of the grant date	33.00%
Weighted average fair values of share-based awards granted (in dollars per share)	$ 57.82	$ 64.32	$ 55.97
Stock Appreciation Rights (SARs) \| Cliff Vesting
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Period awards become fully vested or exercisable period	3 years
Share-Based Awards
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total compensation cost not yet recognized related to non-vested awards	$ 16,700,000
Period for recognition	1 year 9 months 21 days
Time-Based Restricted Stock Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Percentage vested after each anniversary of the grant date	33.00%
Period awards become fully vested or exercisable period	3 years
Non-Employee Directors \| Unrestricted Stock
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares granted (in shares)	1,725	1,662	1,475
The 2023 Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of shares reserved for issuance (in shares)				375,000
Shares available for future grants (in shares)	312,887
The 2023 Plan \| Non-Employee Directors \| Stock Appreciation Rights (SARs)
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares granted (in shares)	4,935	4,938	5,004