Stock Based Compensation - Additional Information (Detail) - USD ($) $ in Millions	3 Months Ended	9 Months Ended
May 31, 2022	May 31, 2021	May 31, 2022	May 30, 2022	May 31, 2021
Share-Based Payment Arrangement [Abstract]
Stock based compensation expense	$ 5.0	$ 3.5	$ 10.9	$ 10.9	$ 12.5

Amount of noncash expense for share-based payment arrangement.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 28
-Subparagraph (a)
-URI https://asc.fasb.org/extlink&oid=126954810&loc=d3e3602-108585

Name:	us-gaap_ShareBasedCompensation
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration