Calculation of Earnings Per Share - Schedule of Earnings Per Share (Details) - USD ($) $ / shares in Units, shares in Thousands, $ in Thousands	3 Months Ended		9 Months Ended
	Mar. 02, 2024	Feb. 25, 2023	Mar. 02, 2024	Feb. 25, 2023
Numerator for Basic and Diluted Earnings Per Share:
Net income	$ 750	$ 6,340	$ 180	$ 18,213
Undistributed (loss) earnings	(94)	5,506	(2,352)	15,729
Undistributed (loss) earnings	$ (94)	$ 5,506	$ (2,352)	$ 15,729
Denominator for Basic and Diluted Earnings Per Share:
Effect of dilutive securities dilutive stock options	218	619	272	631
Weighted Average Number of Shares Outstanding, Diluted	12,445	12,666	12,480	12,524
Basic
Numerator for Basic and Diluted Earnings Per Share:
Net income	$ 750	$ 6,340	$ 180	$ 18,213
Diluted
Numerator for Basic and Diluted Earnings Per Share:
Net income	750	6,340	180	18,213
Common Stock
Numerator for Basic and Diluted Earnings Per Share:
Undistributed (loss) earnings	(82)	4,774	(2,043)	13,614
Undistributed (loss) earnings	$ (82)	$ 4,805	$ (2,049)	$ 13,707
Denominator for Basic and Diluted Earnings Per Share:
Weighted Average Number of Shares Outstanding, Basic	12,227	12,047	12,208	11,893
Weighted Average Number of Shares Outstanding, Diluted	12,445	12,666	12,480	12,524
Net income per share:
Earnings Per Share, Basic	$ 0.05	$ 0.46	$ 0.01	$ 1.33
Net income per share:
Earnings Per Share, Diluted	$ 0.05	$ 0.44	$ 0.01	$ 1.27
Common Stock | Basic
Numerator for Basic and Diluted Earnings Per Share:
Less dividends	$ 733	$ 724	$ 2,199	$ 2,152
Common Stock | Diluted
Numerator for Basic and Diluted Earnings Per Share:
Less dividends	733	724	2,199	2,152
Common Class B
Numerator for Basic and Diluted Earnings Per Share:
Undistributed (loss) earnings	(12)	732	(309)	2,115
Undistributed (loss) earnings	$ (12)	$ 701	$ (303)	$ 2,022
Denominator for Basic and Diluted Earnings Per Share:
Weighted Average Number of Shares Outstanding, Basic	2,052	2,052	2,052	2,053
Weighted Average Number of Shares Outstanding, Diluted	2,052	2,052	2,052	2,053
Net income per share:
Earnings Per Share, Basic	$ 0.05	$ 0.41	$ 0.01	$ 1.19
Net income per share:
Earnings Per Share, Diluted	$ 0.05	$ 0.4	$ 0.01	$ 1.15
Common Class B | Basic
Numerator for Basic and Diluted Earnings Per Share:
Less dividends	$ 111	$ 110	$ 333	$ 332
Common Class B | Diluted
Numerator for Basic and Diluted Earnings Per Share:
Less dividends	$ 111	$ 110	$ 333	$ 332