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Business Segments and Foreign Operations (Net Sales and Long-Lived Assets by Geographical Area) (Details) - USD ($)
$ in Thousands
 12 Months Ended
Aug. 31, 2023
Aug. 31, 2022
Aug. 31, 2021
Revenues from External Customers and Long-Lived Assets [Line Items]      
Net sales $ 537,255 $ 518,820 $ 488,109
Long-lived assets 66,791 65,977 70,145
United States      
Revenues from External Customers and Long-Lived Assets [Line Items]      
Net sales 207,629 176,863 164,946
Long-lived assets 33,263 35,375 37,204
International      
Revenues from External Customers and Long-Lived Assets [Line Items]      
Net sales 329,626 341,957 323,163
Long-lived assets $ 33,528 $ 30,602 $ 32,941