Employee Benefit Plans - Components of Net Periodic Benefit Cost (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 27, 2022	Aug. 28, 2021	Aug. 29, 2020
Pension Plans
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]
Service cost	$ 72	$ 71	$ 113
Interest cost	104	104	131
Expected return on assets	$ (118)	$ (131)	$ (138)
Defined Benefit Plan, Net Periodic Benefit Cost (Credit) Excluding Service Cost, Statement of Income or Comprehensive Income [Extensible Enumeration]	Other Comprehensive (Income) Loss, Defined Benefit Plan, after Tax and Reclassification Adjustment, Attributable to Parent	Other Comprehensive (Income) Loss, Defined Benefit Plan, after Tax and Reclassification Adjustment, Attributable to Parent	Other Comprehensive (Income) Loss, Defined Benefit Plan, after Tax and Reclassification Adjustment, Attributable to Parent
Amortization of prior service cost	$ 21	$ 55	$ 66
Amortization of net loss	20	36	12
Other events	(10)	49
Net periodic benefit cost	89	184	184
SERP
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]
Service cost	919	1,100	918
Interest cost	928	943	1,027
Amortization of net loss	516	821	703
Other events	(855)
Net periodic benefit cost	$ 1,508	$ 2,864	$ 2,648