Accumulated Other Comprehensive Loss - Components of Accumulated Other Comprehensive Loss, Net of Tax (Details) - USD ($) $ in Thousands		3 Months Ended		9 Months Ended
		May 29, 2021	May 30, 2020	May 29, 2021	May 30, 2020
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		$ 1,801,110	$ 1,701,438	$ 1,741,129
Other comprehensive income (loss)		6,047	(3,803)	9,524	$ (3,216)
Balance at end of period		1,845,199	1,708,100	1,845,199	1,708,100
Foreign Currency Translation
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(18,455)	(24,420)	(22,009)	(24,640)
Other comprehensive income (loss) before reclassification		6,099	(3,835)	9,653	(3,615)
Amounts reclassified from accumulated other comprehensive loss		0	0	0	0
Other comprehensive income (loss)		6,099	(3,835)	9,653	(3,615)
Balance at end of period		(12,356)	(28,255)	(12,356)	(28,255)
Pension-related
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	(10,026)	(8,889)	(10,026)	(9,239)
Other comprehensive income (loss) before reclassification	[1]	0	0	0	0
Amounts reclassified from accumulated other comprehensive loss	[1]	0	0	0	350
Other comprehensive income (loss)	[1]	0	0	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]	(12)	208	65	191
Other comprehensive income (loss) before reclassification	[1]	(91)	79	(158)	156
Amounts reclassified from accumulated other comprehensive loss	[1]	39	(47)	29	(107)
Other comprehensive income (loss)	[1]	(52)	32	(129)	49
Balance at end of period	[1]	(64)	240	(64)	240
Accumulated Other Comprehensive Loss
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(28,493)	(33,101)	(31,970)	(33,688)
Other comprehensive income (loss) before reclassification		6,008	(3,756)	9,495	(3,459)
Amounts reclassified from accumulated other comprehensive loss		39	(47)	29	243
Other comprehensive income (loss)		6,047	(3,803)	9,524	(3,216)
Balance at end of period		$ (22,446)	$ (36,904)	$ (22,446)	$ (36,904)

[1] Amounts are shown net of tax