Net Income Per Share (Details) - USD ($) $ / shares in Units, $ in Thousands	3 Months Ended		9 Months Ended
	May 31, 2022	May 31, 2021	May 31, 2022	May 31, 2021
Basic Earnings per Share
Net income	$ 15,545	$ 14,289	$ 34,398	$ 34,297
Less: Allocated to participating securities	104	94	228	239
Net income available to common shareholders	$ 15,441	$ 14,195	$ 34,170	$ 34,058
Basic weighted average shares outstanding	9,399,231	9,386,814	9,398,778	9,381,433
Net income per share - Basic (in dollars per share)	$ 1.64	$ 1.51	$ 3.64	$ 3.63
Diluted Earnings per Share
Net income	$ 15,545	$ 14,289	$ 34,398	$ 34,297
Less: Allocated to participating securities	104	94	228	239
Net income available to common shareholders	$ 15,441	$ 14,195	$ 34,170	$ 34,058
Basic weighted average shares outstanding	9,399,231	9,386,814	9,398,778	9,381,433
Additional dilutive common stock equivalents (in shares)	32,028	48,521	36,591	45,446
Diluted weighted average shares outstanding	9,431,259	9,435,335	9,435,369	9,426,879
Net income per share - Diluted (in dollars per share)	$ 1.64	$ 1.50	$ 3.62	$ 3.61
Antidilutive securities
Antidilutive stock options excluded from computation of earnings per share amount (in shares)	108,392	17,947	93,869	59,346