Condensed Consolidated Statements of Equity - USD ($) shares in Thousands, $ in Thousands	Total	Class A Common Stock	Class B Common Stock	Common Stock Class A Common Stock	Common Stock Class B Common Stock	Additional Paid-in Capital	Retained Earnings	Accumulated Other Comprehensive Loss	Total SSI Shareholders' Equity	Noncontrolling Interests
Beginning balance at Aug. 31, 2020	$ 680,436			$ 26,899	$ 200	$ 36,616	$ 649,863	$ (36,871)	$ 676,707	$ 3,729
Beginning balance (in shares) at Aug. 31, 2020				26,899	200
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	126,179						122,327		122,327	3,852
Other comprehensive income, net of tax	6,140							6,140	6,140
Distributions to noncontrolling interests	(3,029)									(3,029)
Issuance of restricted stock				$ 644		(644)
Issuance of restricted stock (in shares)				644
Restricted stock withheld for taxes	(5,435)			$ (220)		(5,215)			(5,435)
Restricted stock withheld for taxes (in shares)				(220)
Share-based compensation cost	14,220					14,220			14,220
Dividends	(15,928)						(15,928)		(15,928)
Ending balance at May. 31, 2021	802,583			$ 27,323	$ 200	44,977	756,262	(30,731)	798,031	4,552
Ending balance (in shares) at May. 31, 2021				27,323	200
Beginning balance at Feb. 28, 2021	734,039			$ 27,263	$ 200	39,695	697,966	(35,282)	729,842	4,197
Beginning balance (in shares) at Feb. 28, 2021				27,263	200
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	65,436						63,635		63,635	1,801
Other comprehensive income, net of tax	4,551							4,551	4,551
Distributions to noncontrolling interests	(1,446)									(1,446)
Issuance of restricted stock				$ 91		(91)
Issuance of restricted stock (in shares)				91
Restricted stock withheld for taxes	(1,464)			$ (31)		(1,433)			(1,464)
Restricted stock withheld for taxes (in shares)				(31)
Share-based compensation cost	6,806					6,806			6,806
Dividends	(5,339)						(5,339)		(5,339)
Ending balance at May. 31, 2021	802,583			$ 27,323	$ 200	44,977	756,262	(30,731)	798,031	4,552
Ending balance (in shares) at May. 31, 2021				27,323	200
Beginning balance at Aug. 31, 2021	839,779			$ 27,332	$ 200	49,074	793,712	(34,554)	835,764	4,015
Beginning balance (in shares) at Aug. 31, 2021		27,332	200	27,332	200
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	160,945						158,448		158,448	2,497
Other comprehensive income, net of tax	309							309	309
Distributions to noncontrolling interests	(2,330)									(2,330)
Share repurchases	(17,858)			$ (444)		(17,414)			(17,858)
Share repurchase (in shares)				(444)
Issuance of restricted stock				$ 568		(568)
Issuance of restricted stock (in shares)				568
Restricted stock withheld for taxes	(11,003)			$ (209)		(10,794)			(11,003)
Restricted stock withheld for taxes (in shares)				(209)
Share-based compensation cost	14,128					14,128			14,128
Dividends	(16,100)						(16,100)		(16,100)
Ending balance at May. 31, 2022	967,870			$ 27,247	$ 200	34,426	936,060	(34,245)	963,688	4,182
Ending balance (in shares) at May. 31, 2022		27,247	200	27,247	200
Beginning balance at Feb. 28, 2022	904,649			$ 27,433	$ 200	40,821	866,776	(34,438)	900,792	3,857
Beginning balance (in shares) at Feb. 28, 2022				27,433	200
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income	75,504						74,634		74,634	870
Other comprehensive income, net of tax	193							193	193
Distributions to noncontrolling interests	(545)									(545)
Share repurchases	(9,993)			$ (244)		(9,749)			(9,993)
Share repurchase (in shares)				(244)
Issuance of restricted stock				$ 89		(89)
Issuance of restricted stock (in shares)				89
Restricted stock withheld for taxes	(1,426)			$ (31)		(1,395)			(1,426)
Restricted stock withheld for taxes (in shares)				(31)
Share-based compensation cost	4,838					4,838			4,838
Dividends	(5,350)						(5,350)		(5,350)
Ending balance at May. 31, 2022	$ 967,870			$ 27,247	$ 200	$ 34,426	$ 936,060	$ (34,245)	$ 963,688	$ 4,182
Ending balance (in shares) at May. 31, 2022		27,247	200	27,247	200