Accumulated Other Comprehensive Loss - Components of Accumulated Other Comprehensive Loss, Net of Tax (Details) - USD ($)		3 Months Ended		6 Months Ended
		Feb. 25, 2023	Feb. 26, 2022	Feb. 25, 2023	Feb. 26, 2022
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		$ 1,941,966,000	$ 1,894,901,000	$ 1,915,871,000	$ 1,872,952,000
Other comprehensive (loss) income		(1,414,000)	1,094,000	(3,140,000)	(1,658,000)
Balance at end of period		1,955,088,000	1,898,975,000	1,955,088,000	1,898,975,000
Foreign Currency Translation
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(26,581,000)	(20,600,000)	(24,803,000)	(17,801,000)
Other comprehensive (loss) income before reclassification		(1,473,000)	1,149,000	(3,251,000)	(1,650,000)
Amounts reclassified from accumulated other comprehensive loss		0	0	0	0
Other comprehensive (loss) income		(1,473,000)	1,149,000	(3,251,000)	(1,650,000)
Balance at end of period		(28,054,000)	(19,451,000)	(28,054,000)	(19,451,000)
Pension-related
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	452,000	(7,066,000)	452,000	(7,066,000)
Other comprehensive (loss) income before reclassification	[1]	0	0	0	0
Amounts reclassified from accumulated other comprehensive loss	[1]	0	0	0	0
Other comprehensive (loss) income	[1]	0	0	0	0
Balance at end of period	[1]	452,000	(7,066,000)	452,000	(7,066,000)
Derivative Financial Instruments
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	113,000	78,000	61,000	31,000
Other comprehensive (loss) income before reclassification	[1]	84,000	(40,000)	156,000	45,000
Amounts reclassified from accumulated other comprehensive loss	[1]	(25,000)	(15,000)	(45,000)	(53,000)
Other comprehensive (loss) income	[1]	59,000	(55,000)	111,000	(8,000)
Balance at end of period	[1]	172,000	23,000	172,000	23,000
Accumulated Other Comprehensive Loss
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(26,016,000)	(27,588,000)	(24,290,000)	(24,836,000)
Other comprehensive (loss) income before reclassification		(1,389,000)	1,109,000	(3,095,000)	(1,605,000)
Amounts reclassified from accumulated other comprehensive loss		(25,000)	(15,000)	(45,000)	(53,000)
Other comprehensive (loss) income		(1,414,000)	1,094,000	(3,140,000)	(1,658,000)
Balance at end of period		$ (27,430,000)	$ (26,494,000)	$ (27,430,000)	$ (26,494,000)

[1] Amounts are shown net of tax