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Accumulated Other Comprehensive Loss - Changes in AOCI by Component (Details) - USD ($)
$ in Thousands
12 Months Ended
Aug. 27, 2022
Aug. 28, 2021
Aug. 29, 2020
Accumulated Other Comprehensive Income (Loss) [Roll Forward]      
Balance at beginning of year $ 1,056,943 $ 827,466 $ 632,212
Other comprehensive income (loss) 37 35 (35)
Balance at end of year 1,263,007 1,056,943 827,466
Defined Benefit Pension Items      
Accumulated Other Comprehensive Income (Loss) [Roll Forward]      
Balance at beginning of year (491) (526)  
OCI before reclassifications 0 0  
Amounts reclassified from AOCI 37 35  
Other comprehensive income (loss) 37 35  
Balance at end of year $ (454) $ (491) $ (526)