RESTRUCTURING ACTIVITIES (Liabilities for Initiatives and Changes) (Details) - SCAE Plan $ in Millions	6 Months Ended
	Nov. 29, 2015 USD ($)
Restructuring Cost and Reserve [Roll Forward]
Balance at Beginning of Period	$ 32.3
Costs Incurred and Charged to Expense	96.0
Costs Paid or Otherwise Settled	(23.3)
Changes in Estimates	(1.3)
Balance at End of Period	103.7
Multi-employer pension costs
Restructuring Cost and Reserve [Roll Forward]
Balance at Beginning of Period	11.4
Costs Incurred and Charged to Expense	0.2
Costs Paid or Otherwise Settled	(0.4)
Changes in Estimates	0.0
Balance at End of Period	11.2
Severance
Restructuring Cost and Reserve [Roll Forward]
Balance at Beginning of Period	16.4
Costs Incurred and Charged to Expense	63.3
Costs Paid or Otherwise Settled	(11.6)
Changes in Estimates	(0.6)
Balance at End of Period	67.5
Consulting
Restructuring Cost and Reserve [Roll Forward]
Balance at Beginning of Period	0.2
Costs Incurred and Charged to Expense	25.3
Costs Paid or Otherwise Settled	(6.6)
Changes in Estimates	0.0
Balance at End of Period	18.9
Contract cancellation
Restructuring Cost and Reserve [Roll Forward]
Balance at Beginning of Period	3.1
Costs Incurred and Charged to Expense	3.3
Costs Paid or Otherwise Settled	(1.0)
Changes in Estimates	(0.6)
Balance at End of Period	4.8
Other costs
Restructuring Cost and Reserve [Roll Forward]
Balance at Beginning of Period	1.2
Costs Incurred and Charged to Expense	3.9
Costs Paid or Otherwise Settled	(3.7)
Changes in Estimates	(0.1)
Balance at End of Period	$ 1.3