Accumulated Other Comprehensive Loss - Components of Accumulated Other Comprehensive Loss, Net of Tax (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Feb. 24, 2024	Feb. 25, 2023	Feb. 24, 2024	Feb. 25, 2023
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		$ 2,040,173	$ 1,941,966	$ 2,003,960	$ 1,915,871
Other comprehensive income (loss)		885	(1,414)	722	(3,140)
Balance at end of period		2,049,685	1,955,088	2,049,685	1,955,088
Foreign Currency Translation
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(26,655)	(26,581)	(26,504)	(24,803)
Other comprehensive income (loss) before reclassification		919	(1,473)	768	(3,251)
Amounts reclassified from accumulated other comprehensive loss		0	0	0	0
Other comprehensive income (loss)		919	(1,473)	768	(3,251)
Balance at end of period		(25,736)	(28,054)	(25,736)	(28,054)
Pension-related
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	2,582	452	2,582	452
Other comprehensive income (loss) before reclassification	[1]	0	0	0	0
Amounts reclassified from accumulated other comprehensive loss	[1]	0	0	0	0
Other comprehensive income (loss)	[1]	0	0	0	0
Balance at end of period	[1]	2,582	452	2,582	452
Derivative Financial Instruments
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	149	113	161	61
Other comprehensive income (loss) before reclassification	[1]	(14)	84	(2)	156
Amounts reclassified from accumulated other comprehensive loss	[1]	(20)	(25)	(44)	(45)
Other comprehensive income (loss)	[1]	(34)	59	(46)	111
Balance at end of period	[1]	115	172	115	172
Accumulated Other Comprehensive Loss
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(23,924)	(26,016)	(23,761)	(24,290)
Other comprehensive income (loss) before reclassification		905	(1,389)	766	(3,095)
Amounts reclassified from accumulated other comprehensive loss		(20)	(25)	(44)	(45)
Other comprehensive income (loss)		885	(1,414)	722	(3,140)
Balance at end of period		$ (23,039)	$ (27,430)	$ (23,039)	$ (27,430)

[1] Amounts are shown net of tax