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Income Per Share - Schedule of Computation of Basic Income Per Share (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands | 3 Months Ended
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Nov. 30, 2019 | Nov. 24, 2018
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items] |  |
Net income available to shareholders | $ 48,242 | $ 38,320
Allocation of net income for Basic: |  |
Common stock | $ 48,242 | $ 38,320
Weighted average number of shares for Basic: |  |
Common stock (in shares) | 18,951 | 19,142
Common Stock |  |
Allocation of net income for Basic: |  |
Common stock | $ 40,526 | $ 32,137
Weighted average number of shares for Basic: |  |
Common stock (in shares) | 15,308 | 15,432
Income per share for Basic: |  |
Common stock (in dollars per share) | $ 2.65 | $ 2.08
Class B Common Stock |  |
Allocation of net income for Basic: |  |
Common stock | $ 7,716 | $ 6,183
Weighted average number of shares for Basic: |  |
Common stock (in shares) | 3,643 | 3,710
Income per share for Basic: |  |
Common stock (in dollars per share) | $ 2.12 | $ 1.67

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