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Restructuring, Severance and Related Charges (Summary) (Details) - USD ($)
$ in Thousands
3 Months Ended 6 Months Ended
Feb. 28, 2021
Feb. 29, 2020
Feb. 28, 2021
Feb. 29, 2020
Restructuring Cost and Reserve [Line Items]        
Restructuring, severance and related charges $ 6,626 $ 29,604 $ 4,911 $ 74,855
Operating Segments | EMS        
Restructuring Cost and Reserve [Line Items]        
Restructuring, severance and related charges 2,500 14,700 (500) 32,100
Operating Segments | DMS        
Restructuring Cost and Reserve [Line Items]        
Restructuring, severance and related charges 4,000 14,500 5,000 39,700
Other non-allocated assets        
Restructuring Cost and Reserve [Line Items]        
Restructuring, severance and related charges 100 400 400 3,100
Employee severance and benefit costs        
Restructuring Cost and Reserve [Line Items]        
Restructuring, severance and related charges 2,140 8,012 2,708 26,793
Lease costs        
Restructuring Cost and Reserve [Line Items]        
Restructuring, severance and related charges 0 6,229 (2,873) 6,468
Asset write-off costs        
Restructuring Cost and Reserve [Line Items]        
Restructuring, severance and related charges 4,592 9,109 4,590 25,425
Other Related Costs        
Restructuring Cost and Reserve [Line Items]        
Restructuring, severance and related charges $ (106) $ 6,254 $ 486 $ 16,169