Accumulated Other Comprehensive Loss - Components of Accumulated Other Comprehensive Loss, Net of Tax (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Feb. 26, 2022	Feb. 27, 2021	Feb. 26, 2022	Feb. 27, 2021
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		$ 1,894,901	$ 1,773,352	$ 1,872,952	$ 1,741,129
Other comprehensive income (loss)		1,094	2,188	(1,658)	3,477
Balance at end of period		1,898,975	1,801,110	1,898,975	1,801,110
Foreign Currency Translation
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(20,600)	(20,699)	(17,801)	(22,009)
Other comprehensive income (loss) before reclassification		1,149	2,244	(1,650)	3,554
Amounts reclassified from accumulated other comprehensive loss		0	0	0	0
Other comprehensive income (loss)		1,149	2,244	(1,650)	3,554
Balance at end of period		(19,451)	(18,455)	(19,451)	(18,455)
Pension-related
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	(7,066)	(10,026)	(7,066)	(10,026)
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)	(10,026)	(7,066)	(10,026)
Derivative Financial Instruments
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	78	44	31	65
Other comprehensive income (loss) before reclassification	[1]	(40)	(58)	45	(68)
Amounts reclassified from accumulated other comprehensive loss	[1]	(15)	2	(53)	(9)
Other comprehensive income (loss)	[1]	(55)	(56)	(8)	(77)
Balance at end of period	[1]	23	(12)	23	(12)
Accumulated Other Comprehensive Loss
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(27,588)	(30,681)	(24,836)	(31,970)
Other comprehensive income (loss) before reclassification		1,109	2,186	(1,605)	3,486
Amounts reclassified from accumulated other comprehensive loss		(15)	2	(53)	(9)
Other comprehensive income (loss)		1,094	2,188	(1,658)	3,477
Balance at end of period		$ (26,494)	$ (28,493)	$ (26,494)	$ (28,493)

[1] Amounts are shown net of tax