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Net Income Per Share - Schedule of Computation of Basic Earnings Per Share (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands | 3 Months Ended
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Nov. 25, 2017 | Nov. 26, 2016
Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items] |  |
Net income available to shareholders | $ 34,206 | $ 28,214
Allocation of net income for Basic: |  |
Common Stock | $ 34,206 | $ 28,214
Weighted average number of shares for Basic: |  |
Common Stock (in shares) | 20,278 | 20,272
Common Stock |  |
Allocation of net income for Basic: |  |
Common Stock | $ 27,384 | $ 22,342
Weighted average number of shares for Basic: |  |
Common Stock (in shares) | 15,462 | 15,285
Earnings per share for Basic: |  |
Common Stock (in dollars per share) | $ 1.77 | $ 1.46
Class B Common Stock |  |
Allocation of net income for Basic: |  |
Common Stock | $ 6,822 | $ 5,668
Weighted average number of shares for Basic: |  |
Common Stock (in shares) | 4,816 | 4,847
Earnings per share for Basic: |  |
Common Stock (in dollars per share) | $ 1.42 | $ 1.17
Unvested participating shares |  |
Allocation of net income for Basic: |  |
Common Stock | $ 0 | $ 204
Weighted average number of shares for Basic: |  |
Common Stock (in shares) | 0 | 140

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