Accumulated Other Comprehensive Loss - Components of Accumulated Other Comprehensive Loss, Net of Tax (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Feb. 27, 2021	Feb. 29, 2020	Feb. 27, 2021	Feb. 29, 2020
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		$ 1,773,352	$ 1,676,008	$ 1,741,129	$ 1,641,230
Other comprehensive income (loss)		2,188	(397)	3,477	587
Balance at end of period		1,801,110	1,701,438	1,801,110	1,701,438
Foreign Currency Translation
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(20,699)	(23,651)	(22,009)	(24,640)
Other comprehensive income (loss) before reclassification		2,244	(769)	3,554	220
Amounts reclassified from accumulated other comprehensive loss		0	0	0	0
Other comprehensive income (loss)		2,244	(769)	3,554	220
Balance at end of period		(18,455)	(24,420)	(18,455)	(24,420)
Pension-related
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	(10,026)	(9,239)	(10,026)	(9,239)
Other comprehensive income (loss) before reclassification	[1]	0	0	0	0
Amounts reclassified from accumulated other comprehensive loss	[1]	0	350	0	350
Other comprehensive income (loss)	[1]	0	350	0	350
Balance at end of period	[1]	(10,026)	(8,889)	(10,026)	(8,889)
Derivative Financial Instruments
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	44	186	65	191
Other comprehensive income (loss) before reclassification	[1]	(58)	52	(68)	77
Amounts reclassified from accumulated other comprehensive loss	[1]	2	(30)	(9)	(60)
Other comprehensive income (loss)	[1]	(56)	22	(77)	17
Balance at end of period	[1]	(12)	208	(12)	208
Accumulated Other Comprehensive Loss
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(30,681)	(32,704)	(31,970)	(33,688)
Other comprehensive income (loss) before reclassification		2,186	(717)	3,486	297
Amounts reclassified from accumulated other comprehensive loss		2	320	(9)	290
Other comprehensive income (loss)		2,188	(397)	3,477	587
Balance at end of period		$ (28,493)	$ (33,101)	$ (28,493)	$ (33,101)

[1] Amounts are shown net of tax