Accumulated Other Comprehensive Loss - Components of Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Thousands		12 Months Ended
		Aug. 28, 2021	Aug. 29, 2020	Aug. 31, 2019
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		$ 1,741,129	$ 1,641,230	$ 1,464,967
Change during the year		7,134	1,718	(8,529)
Balance at end of period		1,872,952	1,741,129	1,641,230
Foreign Currency Translation
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(22,009)	(24,640)
Change during the year		4,208	2,631
Balance at end of period		(17,801)	(22,009)	(24,640)
Pension-related
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	(10,026)	(9,239)
Change during the year	[1]	2,960	(787)
Balance at end of period	[1]	(7,066)	(10,026)	(9,239)
Derivative Financial Instruments
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	65	191
Change during the year	[1]	(34)	(126)
Balance at end of period	[1]	31	65	191
Accumulated Other Comprehensive Loss
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(31,970)	(33,688)	(25,159)
Change during the year		7,134	1,718
Balance at end of period		$ (24,836)	$ (31,970)	$ (33,688)

[1] Amounts are shown net of tax