Stockholders' Equity - Narrative (Details) - USD ($)	3 Months Ended		6 Months Ended
	Feb. 29, 2020	Feb. 28, 2019	Feb. 29, 2020	Feb. 28, 2019	Mar. 25, 2020	Mar. 24, 2020
Accumulated Other Comprehensive Income (Loss) [Line Items]
Repurchase of common stock (in shares)	267,500	214,945	610,500	489,945
Repurchases of common stock	$ 74,172,000	$ 44,143,000	$ 158,595,000	$ 104,584,000
Remaining authorized repurchase amount	$ 80,000,000.0		80,000,000.0
Cost of shares repurchased from employees			$ 1,600,000	$ 6,100,000
Subsequent event
Accumulated Other Comprehensive Income (Loss) [Line Items]
Remaining authorized repurchase amount					$ 300,000,000.0
Approved addition to authorized amount						$ 220,000,000.0
Restricted stock units
Accumulated Other Comprehensive Income (Loss) [Line Items]
Restricted stock vested (in shares)			16,476	75,530
Cost of shares repurchased from employees			$ 1,600,000	$ 6,100,000
Treasury Stock
Accumulated Other Comprehensive Income (Loss) [Line Items]
Repurchase of common stock (in shares)	267,500	214,945	610,500	489,945
Repurchases of common stock	$ 74,172,000	$ 44,143,000	$ 158,595,000	$ 104,584,000
Vesting of restricted stock (in shares)	431	8,502
Treasury Stock | Restricted stock units
Accumulated Other Comprehensive Income (Loss) [Line Items]
Vesting of restricted stock (in shares)			6,209	27,852