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Net Income Per Share - Schedule of Computation of Diluted 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, Diluted, by Common Class, Including Two Class Method [Line Items] |  |
As reported - Basic | $ 34,206 | $ 28,214
As reported - Basic (in shares) | 20,278 | 20,272
Add: Undistributed earnings allocated to unvested participating shares | $ 0 | $ 199
Less: Undistributed earnings reallocated to unvested participating shares | 0 | (189)
Diluted EPS – Common Stock | $ 34,206 | $ 28,020
Diluted EPS – Common Stock (in shares) | 20,434 | 20,249
Diluted EPS – Common Stock (in dollars per share) | $ 1.67 | $ 1.38
Common Stock |  |
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items] |  |
As reported - Basic | $ 27,384 | $ 22,342
As reported - Basic (in shares) | 15,462 | 15,285
As reported - Basic (in dollars per share) | $ 1.77 | $ 1.46
Add: effect of dilutive potential common shares | $ 0 | $ 0
Add: effect of dilutive potential common shares (in shares) | 156 | 117
Class B Common Stock |  |
Earnings Per Share, Diluted, by Common Class, Including Two Class Method [Line Items] |  |
As reported - Basic | $ 6,822 | $ 5,668
As reported - Basic (in shares) | 4,816 | 4,847
As reported - Basic (in dollars per share) | $ 1.42 | $ 1.17
Add: effect of dilutive potential common shares | $ 6,822 | $ 5,668
Add: effect of dilutive potential common shares (in shares) | 4,816 | 4,847

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