Condensed Consolidated Statements of Equity - USD ($) shares in Thousands, $ in Thousands	3 Months Ended		9 Months Ended
	May 31, 2023	May 31, 2022	May 31, 2023	May 31, 2022
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	$ 928,438	$ 904,649	$ 958,474	$ 839,779
Net income	13,608	75,504	324	160,945
Other comprehensive Income (loss), net of tax	420	193	(3,096)	309
Distributions to noncontrolling interests	(59)	(545)	(1,214)	(2,330)
Share repurchases		(9,993)		(17,858)
Restricted stock withheld for taxes	(802)	(1,426)	(7,611)	(11,003)
Share-based compensation cost	3,314	4,838	8,487	14,128
Dividends	(5,327)	(5,350)	(15,772)	(16,100)
Ending balance	$ 939,592	967,870	$ 939,592	967,870
Class A Common Stock
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance (in shares)			26,747
Ending balance (in shares)	27,311		27,311
Class B Common Stock
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance (in shares)			200
Ending balance (in shares)	200		200
Common Stock | Class A Common Stock
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	$ 27,255	$ 27,433	$ 26,747	$ 27,332
Beginning balance (in shares)	27,255	27,433	26,747	27,332
Share repurchases		$ (244)		$ (444)
Share repurchase (in shares)		(244)		(444)
Issuance of restricted stock	$ 84	$ 89	$ 846	$ 568
Issuance of restricted stock (in shares)	84	89	846	568
Restricted stock withheld for taxes	$ (28)	$ (31)	$ (282)	$ (209)
Restricted stock withheld for taxes (in shares)	(28)	(31)	(282)	(209)
Ending balance	$ 27,311	$ 27,247	$ 27,311	$ 27,247
Ending balance (in shares)	27,311	27,247	27,311	27,247
Common Stock | Class B Common Stock
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	$ 200	$ 200	$ 200	$ 200
Beginning balance (in shares)	200	200	200	200
Ending balance	$ 200	$ 200	$ 200	$ 200
Ending balance (in shares)	200	200	200	200
Additional Paid-in Capital
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	$ 20,831	$ 40,821	$ 22,975	$ 49,074
Share repurchases		(9,749)		(17,414)
Issuance of restricted stock	(84)	(89)	(846)	(568)
Restricted stock withheld for taxes	(774)	(1,395)	(7,329)	(10,794)
Share-based compensation cost	3,314	4,838	8,487	14,128
Ending balance	23,287	34,426	23,287	34,426
Retained Earnings
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	917,266	866,776	941,146	793,712
Net income	13,460	74,634	25	158,448
Dividends	(5,327)	(5,350)	(15,772)	(16,100)
Ending balance	925,399	936,060	925,399	936,060
Accumulated Other Comprehensive Loss
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	(40,605)	(34,438)	(37,089)	(34,554)
Other comprehensive Income (loss), net of tax	420	193	(3,096)	309
Ending balance	(40,185)	(34,245)	(40,185)	(34,245)
Total SSI Shareholders' Equity
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	924,947	900,792	953,979	835,764
Net income	13,460	74,634	25	158,448
Other comprehensive Income (loss), net of tax	420	193	(3,096)	309
Share repurchases		(9,993)		(17,858)
Restricted stock withheld for taxes	(802)	(1,426)	(7,611)	(11,003)
Share-based compensation cost	3,314	4,838	8,487	14,128
Dividends	(5,327)	(5,350)	(15,772)	(16,100)
Ending balance	936,012	963,688	936,012	963,688
Noncontrolling Interests
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	3,491	3,857	4,495	4,015
Net income	148	870	299	2,497
Distributions to noncontrolling interests	(59)	(545)	(1,214)	(2,330)
Ending balance	$ 3,580	$ 4,182	$ 3,580	$ 4,182