Accumulated Other Comprehensive Loss - Components of Accumulated Other Comprehensive Loss, Net of Tax (Details) - USD ($) $ in Thousands		3 Months Ended
		Nov. 27, 2021	Nov. 28, 2020
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		$ 1,872,952	$ 1,741,129
Other comprehensive income (loss)		(2,752)	1,289
Balance at end of period		1,894,901	1,773,352
Foreign Currency Translation
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(17,801)	(22,009)
Other comprehensive income (loss) before reclassification		(2,799)	1,310
Amounts reclassified from accumulated other comprehensive loss		0	0
Other comprehensive income (loss)		(2,799)	1,310
Balance at end of period		(20,600)	(20,699)
Pension-related
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	(7,066)	(10,026)
Other comprehensive income (loss) before reclassification	[1]	0	0
Amounts reclassified from accumulated other comprehensive loss	[1]	0	0
Other comprehensive income (loss)	[1]	0	0
Balance at end of period	[1]	(7,066)	(10,026)
Derivative Financial Instruments
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	31	65
Other comprehensive income (loss) before reclassification	[1]	85	(10)
Amounts reclassified from accumulated other comprehensive loss	[1]	(38)	(11)
Other comprehensive income (loss)	[1]	47	(21)
Balance at end of period	[1]	78	44
Accumulated Other Comprehensive Loss
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(24,836)	(31,970)
Other comprehensive income (loss) before reclassification		(2,714)	1,300
Amounts reclassified from accumulated other comprehensive loss		(38)	(11)
Other comprehensive income (loss)		(2,752)	1,289
Balance at end of period		$ (27,588)	$ (30,681)

[1] Amounts are shown net of tax