STOCKHOLDERS' EQUITY - Changes in AOCI (Details) $ in Millions	6 Months Ended
	Nov. 28, 2021 USD ($)
Changes in AOCI:
Balance at the beginning of the period	$ 480.6
Balance at the end of the period	365.2
Accumulated Other Comprehensive Income (Loss)
Changes in AOCI:
Balance at the beginning of the period	29.5
Other comprehensive income before reclassifications, net of tax	(37.2)
Amounts reclassified out of AOCI, net of tax	0.2
Net current-period other comprehensive income (loss)	(37.0)
Balance at the end of the period	(7.5)
Foreign Currency Translation Gains (Losses)
Changes in AOCI:
Balance at the beginning of the period	36.0
Other comprehensive income before reclassifications, net of tax	(37.2)
Net current-period other comprehensive income (loss)	(37.2)
Balance at the end of the period	(1.2)
Pension and Post-Retirement Benefits
Changes in AOCI:
Balance at the beginning of the period	(6.5)
Amounts reclassified out of AOCI, net of tax	0.2
Net current-period other comprehensive income (loss)	0.2
Balance at the end of the period	$ (6.3)