Income Taxes - Additional Information (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Feb. 28, 2025	Feb. 29, 2024	Feb. 28, 2025	Feb. 29, 2024
Income Tax Disclosure Additional Details [Table] [Line Items]
Income tax (benefit) expense	$ 6,798	$ 7,396	$ 12,951	$ 13,064
Effective Income Tax Rate Reconciliation, Percent	24.50%	29.30%	23.30%	26.50%
Federal Statutory Income Tax Rate, Percent			21.00%
Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest	$ 27,699	$ 25,267	$ 55,575	$ 49,241