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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. 24, 2018 | Nov. 25, 2017
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items] |  |
Net income available to shareholders | $ 38,320 | $ 34,206
Allocation of net income for Basic: |  |
Common stock | $ 38,320 | $ 34,206
Weighted average number of shares for Basic: |  |
Common stock (in shares) | 19,142 | 20,278
Common Stock |  |
Allocation of net income for Basic: |  |
Common stock | $ 32,137 | $ 27,384
Weighted average number of shares for Basic: |  |
Common stock (in shares) | 15,432 | 15,462
Income per share for Basic: |  |
Common stock (in dollars per share) | $ 2.08 | $ 1.77
Class B Common Stock |  |
Allocation of net income for Basic: |  |
Common stock | $ 6,183 | $ 6,822
Weighted average number of shares for Basic: |  |
Common stock (in shares) | 3,710 | 4,816
Income per share for Basic: |  |
Common stock (in dollars per share) | $ 1.67 | $ 1.42

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