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Employee Benefit Plans - Weighted Average Assumptions Used in Calculating Net Periodic Benefit Cost (Details)
12 Months Ended
Aug. 26, 2023
Aug. 27, 2022
Aug. 28, 2021
Pension Plans      
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]      
Discount rate 4.30% 2.30% 2.00%
Expected return on plan assets 3.50% 3.50% 3.50%
SERP      
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]      
Discount rate 4.40% 2.60% 2.50%
Rate of compensation increase 5.00% 5.00% 5.00%