Accumulated Other Comprehensive Loss - Components of Accumulated Other Comprehensive Loss, Net of Tax (Details) - USD ($) $ in Thousands		3 Months Ended		9 Months Ended
		May 30, 2020	May 25, 2019	May 30, 2020	May 25, 2019
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		$ 1,701,438	$ 1,580,790	$ 1,641,230	$ 1,464,967
Other comprehensive income (loss)		(3,803)	(2,511)	(3,216)	(3,358)
Balance at end of period		1,708,100	1,609,696	1,708,100	1,609,696
Foreign Currency Translation
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(24,420)	(21,980)	(24,640)	(21,116)
Other comprehensive income (loss) before reclassification		(3,835)	(2,649)	(3,615)	(3,513)
Amounts reclassified from accumulated other comprehensive loss		0	0	0	0
Other comprehensive income (loss)		(3,835)	(2,649)	(3,615)	(3,513)
Balance at end of period		(28,255)	(24,629)	(28,255)	(24,629)
Pension-related
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	(8,889)	(4,135)	(9,239)	(4,135)
Other comprehensive income (loss) before reclassification	[1]	0	0	0	0
Amounts reclassified from accumulated other comprehensive loss	[1]	0	0	350	0
Other comprehensive income (loss)	[1]	0	0	350	0
Balance at end of period	[1]	(8,889)	(4,135)	(8,889)	(4,135)
Derivative Financial Instruments
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	208	109	191	92
Other comprehensive income (loss) before reclassification	[1]	79	184	156	277
Amounts reclassified from accumulated other comprehensive loss	[1]	(47)	(46)	(107)	(122)
Other comprehensive income (loss)	[1]	32	138	49	155
Balance at end of period	[1]	240	247	240	247
Accumulated Other Comprehensive Loss
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(33,101)	(26,006)	(33,688)	(25,159)
Other comprehensive income (loss) before reclassification		(3,756)	(2,465)	(3,459)	(3,236)
Amounts reclassified from accumulated other comprehensive loss		(47)	(46)	243	(122)
Other comprehensive income (loss)		(3,803)	(2,511)	(3,216)	(3,358)
Balance at end of period		$ (36,904)	$ (28,517)	$ (36,904)	$ (28,517)

[1] Amounts are shown net of tax.