Leases - Supplemental Cash Flow Information Related to Leases (Detail) $ in Millions	6 Months Ended
Feb. 29, 2024 USD ($)
Cash Flow, Operating Activities, Lessee [Abstract]
Operating cash flows from operating leases	$ 8.8
ROU assets obtained in exchange for new operating lease liabilities	$ 7.6

Amount of cash outflow from operating lease, excluding payments to bring another asset to condition and location necessary for its intended use.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 45
-Paragraph 5
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479041/842-20-45-5

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Subparagraph (g)(1)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147478964/842-20-50-4

Name:	us-gaap_OperatingLeasePayments
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration