Fair Value Measurements - Schedule of Assets or Liabilities Measured at Fair Value on a Recurring Basis (Details) - Fair Value, Measurements, Recurring - USD ($) $ in Thousands	Aug. 27, 2022	Aug. 28, 2021
Assets:
Cash equivalents	$ 197,121	$ 197,081
Pension plan assets	3,291	3,795
Non-qualified deferred compensation plan assets	1,263
Foreign currency forward contracts	83	41
Total assets at fair value	201,758	200,917
Level 1
Assets:
Cash equivalents	197,121	197,081
Pension plan assets	0	0
Foreign currency forward contracts	0	0
Total assets at fair value	197,121	197,081
Level 2
Assets:
Cash equivalents	0	0
Pension plan assets	3,291	3,795
Non-qualified deferred compensation plan assets	1,263
Foreign currency forward contracts	83	41
Total assets at fair value	4,637	3,836
Level 3
Assets:
Cash equivalents	0	0
Pension plan assets	0	0
Foreign currency forward contracts	0	0
Total assets at fair value	$ 0	$ 0