Segment Reporting - Schedule of Net Sales and Gross Profit by Geographic Region (Details) - USD ($) $ in Thousands		3 Months Ended		9 Months Ended
		Mar. 02, 2024	Feb. 25, 2023	Mar. 02, 2024	Feb. 25, 2023
Segment Reporting Information [Line Items]
Net Sales		$ 52,375	$ 70,364	$ 149,086	$ 203,826
Gross Profit		15,436	22,405	45,242	67,283
North America
Segment Reporting Information [Line Items]
Net Sales		21,456	29,721	57,772	93,126
Gross Profit		8,362	11,463	21,620	36,926
Asia/Pacific
Segment Reporting Information [Line Items]
Net Sales		12,116	14,999	34,988	47,859
Gross Profit		2,902	4,664	10,217	14,985
Europe
Segment Reporting Information [Line Items]
Net Sales		16,081	15,886	46,542	47,816
Gross Profit		4,824	5,132	14,105	14,417
Latin America
Segment Reporting Information [Line Items]
Net Sales		2,732	9,771	8,237	15,077
Gross Profit		1,018	2,508	3,004	4,410
Other
Segment Reporting Information [Line Items]
Net Sales	[1]	(10)	(13)	1,547	(52)
Gross Profit	[1]	$ (1,670)	$ (1,362)	$ (3,704)	$ (3,455)

[1] Other includes primarily net sales not allocated to a specific geographical region, unabsorbed value-add costs and other unallocated expenses.