Accumulated Other Comprehensive Loss - Changes in AOCI by Component (Details) - USD ($) $ in Thousands	12 Months Ended
	Aug. 28, 2021	Aug. 29, 2020	Aug. 31, 2019
Accumulated Other Comprehensive Income (Loss) [Roll Forward]
Balance at beginning of year	$ 827,466	$ 632,212	$ 534,445
OCI before reclassifications	0	(500)
Amounts reclassified from AOCI	35	465
Other comprehensive income (loss)	35	(35)	(1,383)
Balance at end of year	1,056,943	827,466	632,212
Total
Accumulated Other Comprehensive Income (Loss) [Roll Forward]
Balance at beginning of year	(526)	(491)	892
Balance at end of year	(491)	(526)	(491)
Defined Benefit Pension Items
Accumulated Other Comprehensive Income (Loss) [Roll Forward]
Balance at beginning of year	(526)	(559)
OCI before reclassifications	0	0
Amounts reclassified from AOCI	35	33
Other comprehensive income (loss)	35	33
Balance at end of year	(491)	(526)	(559)
Interest Rate Swap
Accumulated Other Comprehensive Income (Loss) [Roll Forward]
Balance at beginning of year	$ 0	68
OCI before reclassifications		(500)
Amounts reclassified from AOCI		432
Other comprehensive income (loss)		(68)
Balance at end of year		$ 0	$ 68