Accumulated Other Comprehensive Loss - Components of Accumulated Other Comprehensive Loss, Net of Tax (Details) - USD ($) $ in Thousands		3 Months Ended		9 Months Ended
		May 25, 2024	May 27, 2023	May 25, 2024	May 27, 2023
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		$ 2,049,685	$ 1,955,088	$ 2,003,960	$ 1,915,871
Other comprehensive (loss) income		(592)	768	130	(2,372)
Balance at end of period		2,075,608	1,976,851	2,075,608	1,976,851
Foreign Currency Translation
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(25,736)	(28,054)	(26,504)	(24,803)
Other comprehensive income (loss) before reclassification		(598)	762	170	(2,489)
Amounts reclassified from accumulated other comprehensive loss		0	0	0	0
Other comprehensive (loss) income		(598)	762	170	(2,489)
Balance at end of period		(26,334)	(27,292)	(26,334)	(27,292)
Pension-related
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	2,582	452	2,582	452
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 (loss) income	[1]	0	0	0	0
Balance at end of period	[1]	2,582	452	2,582	452
Derivative Financial Instruments
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	115	172	161	61
Other comprehensive income (loss) before reclassification	[1]	30	31	28	186
Amounts reclassified from accumulated other comprehensive loss	[1]	(24)	(25)	(68)	(69)
Other comprehensive (loss) income	[1]	6	6	(40)	117
Balance at end of period	[1]	121	178	121	178
Accumulated Other Comprehensive Loss
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(23,039)	(27,430)	(23,761)	(24,290)
Other comprehensive income (loss) before reclassification		(568)	793	198	(2,303)
Amounts reclassified from accumulated other comprehensive loss		(24)	(25)	(68)	(69)
Other comprehensive (loss) income		(592)	768	130	(2,372)
Balance at end of period		$ (23,631)	$ (26,662)	$ (23,631)	$ (26,662)

[1] Amounts are shown net of tax