Accumulated Other Comprehensive Loss - Components of Accumulated Other Comprehensive Loss, Net of Tax (Details) - USD ($)		3 Months Ended		9 Months Ended
		May 28, 2022	May 29, 2021	May 28, 2022	May 29, 2021
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		$ 1,898,975,000	$ 1,801,110,000	$ 1,872,952,000	$ 1,741,129,000
Other comprehensive income (loss)		(996,000)	6,047,000	(2,653,000)	9,524,000
Balance at end of period		1,904,011,000	1,845,199,000	1,904,011,000	1,845,199,000
Foreign Currency Translation
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(19,451,000)	(18,455,000)	(17,801,000)	(22,009,000)
Other comprehensive income (loss) before reclassification		(982,000)	6,099,000	(2,632,000)	9,653,000
Amounts reclassified from accumulated other comprehensive loss		0	0	0	0
Other comprehensive income (loss)		(982,000)	6,099,000	(2,632,000)	9,653,000
Balance at end of period		(20,433,000)	(12,356,000)	(20,433,000)	(12,356,000)
Pension-related
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	(7,066,000)	(10,026,000)	(7,066,000)	(10,026,000)
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]	(7,066,000)	(10,026,000)	(7,066,000)	(10,026,000)
Derivative Financial Instruments
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	23,000	(12,000)	31,000	65,000
Other comprehensive income (loss) before reclassification	[1]	(10,000)	(91,000)	35,000	(158,000)
Amounts reclassified from accumulated other comprehensive loss	[1]	(4,000)	39,000	(57,000)	29,000
Other comprehensive income (loss)	[1]	(14,000)	(52,000)	(22,000)	(129,000)
Balance at end of period	[1]	9,000	(64,000)	9,000	(64,000)
Accumulated Other Comprehensive Loss
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(26,494,000)	(28,493,000)	(24,836,000)	(31,970,000)
Other comprehensive income (loss) before reclassification		(992,000)	6,008,000	(2,597,000)	9,495,000
Amounts reclassified from accumulated other comprehensive loss		(4,000)	39,000	(57,000)	29,000
Other comprehensive income (loss)		(996,000)	6,047,000	(2,654,000)	9,524,000
Balance at end of period		$ (27,490,000)	$ (22,446,000)	$ (27,490,000)	$ (22,446,000)

[1] Amounts are shown net of tax