Stock-Based Compensation Plans - Stock Option Activity (Details) $ / shares in Units, $ in Thousands	12 Months Ended
	Aug. 26, 2023 USD ($) $ / shares shares
Stock Options
Outstanding beginning balance (in shares) | shares	322,107
Granted (in shares) | shares	66,873
Exercised (in shares) | shares	0
Forfeited/canceled (in shares) | shares	0
Outstanding ending balance (in shares) | shares	388,980
Exercisable at end of year (in shares) | shares	278,339
Weighted Average Exercise Price Per Share
Outstanding beginning balance (in dollars per share) | $ / shares	$ 44.75
Granted (in dollars per share) | $ / shares	56.09
Exercised (in dollars per share) | $ / shares	0
Forfeited/canceled (in dollars per share) | $ / shares	0
Outstanding ending balance (in dollars per share) | $ / shares	46.70
Exercisable at end of year (in dollars per share) | $ / shares	$ 41.17
Weighted Average Remaining Contractual Term (in years)
Outstanding	6 years 2 months 12 days
Exercisable	5 years 2 months 12 days
Aggregate Intrinsic Value
Outstanding | $	$ 7,077
Exercisable | $	$ 6,417