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Debt and Lines of Credit (Details)
3 Months Ended 9 Months Ended
Jun. 29, 2018
USD ($)
installment
May 31, 2019
USD ($)
May 31, 2018
USD ($)
May 31, 2019
USD ($)
May 31, 2018
USD ($)
Aug. 31, 2018
USD ($)
Interest Revenue (Expense), Net [Abstract]            
Interest expense   $ 9,100,000 $ 8,900,000 $ 27,400,000 $ 26,300,000  
Interest income   (800,000) (500,000) (1,800,000) (1,800,000)  
Interest expense, net   8,300,000 $ 8,400,000 25,600,000 $ 24,500,000  
Lines of Credit            
Line of Credit Facility [Abstract]            
Executed revolving credit facility $ 800,000,000.0          
Minimum interest coverage ratio 2.50          
Maximum leverage ratio 3.50          
Outstanding letters of credit   9,500,000   9,500,000    
Lines of Credit | Minimum            
Line of Credit Facility [Abstract]            
Facility fee (percent) 0.125%          
Lines of Credit | Maximum            
Line of Credit Facility [Abstract]            
Facility fee (percent) 0.25%          
Lines of Credit | New Revolving Credit Facility            
Line of Credit Facility [Abstract]            
Executed revolving credit facility $ 400,000,000.0          
Revolving credit facility term 5 years          
Borrowings outstanding   0   0    
Lines of Credit | Unsecured Delayed Draw Term Loan            
Line of Credit Facility [Abstract]            
Executed revolving credit facility $ 400,000,000.0          
Number of separate installments allowed during borrowing period | installment 4          
Lines of Credit | Previous Credit Facility            
Line of Credit Facility [Abstract]            
Borrowings outstanding           $ 0
Lines of Credit | Revolving Credit Facility Maturing August 27, 2019            
Line of Credit Facility [Abstract]            
Additional borrowing capacity under revolving credit facility   794,700,000   794,700,000    
Letters of Credit | Revolving Credit Facility Maturing August 27, 2019            
Line of Credit Facility [Abstract]            
Outstanding letters of credit   5,300,000   5,300,000    
Senior unsecured public notes | Senior Unsecured Notes Maturing December 2019            
Debt Instruments [Abstract]            
Debt outstanding   $ 350,000,000.0   $ 350,000,000.0    
Interest rate (percent)   6.00%   6.00%    
Amount to be refinanced       $ 341,100,000    
Industrial revenue bond | Industrial Revenue Bond Maturing in 2021            
Debt Instruments [Abstract]            
Debt outstanding   $ 4,000,000.0   4,000,000.0    
Bank loans | 2016 Fixed-rate Bank Loans            
Debt Instruments [Abstract]            
Debt outstanding   $ 2,800,000   $ 2,800,000    
Eurocurrency Rate | Lines of Credit | New Revolving Credit Facility | Minimum            
Line of Credit Facility [Abstract]            
Applicable margins based on company's leverage ratio, percentage 1.00%          
Eurocurrency Rate | Lines of Credit | New Revolving Credit Facility | Maximum            
Line of Credit Facility [Abstract]            
Applicable margins based on company's leverage ratio, percentage 1.375%          
Eurocurrency Rate | Lines of Credit | Unsecured Delayed Draw Term Loan | Minimum            
Line of Credit Facility [Abstract]            
Applicable margins based on company's leverage ratio, percentage 0.875%          
Eurocurrency Rate | Lines of Credit | Unsecured Delayed Draw Term Loan | Maximum            
Line of Credit Facility [Abstract]            
Applicable margins based on company's leverage ratio, percentage 1.25%          
Base rate | Lines of Credit | New Revolving Credit Facility | Minimum            
Line of Credit Facility [Abstract]            
Applicable margins based on company's leverage ratio, percentage 0.00%          
Base rate | Lines of Credit | New Revolving Credit Facility | Maximum            
Line of Credit Facility [Abstract]            
Applicable margins based on company's leverage ratio, percentage 0.375%          
Base rate | Lines of Credit | Unsecured Delayed Draw Term Loan | Minimum            
Line of Credit Facility [Abstract]            
Applicable margins based on company's leverage ratio, percentage 0.00%          
Base rate | Lines of Credit | Unsecured Delayed Draw Term Loan | Maximum            
Line of Credit Facility [Abstract]            
Applicable margins based on company's leverage ratio, percentage 0.25%          
Year one | Lines of Credit | Unsecured Delayed Draw Term Loan            
Line of Credit Facility [Abstract]            
Quarterly payment (percent) 2.50%          
Year two | Lines of Credit | Unsecured Delayed Draw Term Loan            
Line of Credit Facility [Abstract]            
Quarterly payment (percent) 2.50%          
Year three | Lines of Credit | Unsecured Delayed Draw Term Loan            
Line of Credit Facility [Abstract]            
Quarterly payment (percent) 5.00%          
Year four | Lines of Credit | Unsecured Delayed Draw Term Loan            
Line of Credit Facility [Abstract]            
Quarterly payment (percent) 5.00%          
Year five and after | Lines of Credit | Unsecured Delayed Draw Term Loan            
Line of Credit Facility [Abstract]            
Quarterly payment (percent) 7.50%