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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, 2024
Aug. 31, 2023
Aug. 31, 2022
Revenues from External Customers and Long-Lived Assets [Line Items]      
Net sales $ 590,557 $ 537,255 $ 518,820
Long-lived assets 62,983 66,791 65,977
United States      
Revenues from External Customers and Long-Lived Assets [Line Items]      
Net sales 206,963 207,629 176,863
Long-lived assets 30,057 33,263 35,375
International      
Revenues from External Customers and Long-Lived Assets [Line Items]      
Net sales 383,594 329,626 341,957
Long-lived assets $ 32,926 $ 33,528 $ 30,602