Accumulated Other Comprehensive Income (Changes in Accumulated Other Comprehensive Income (Loss)) (Details) - USD ($) $ in Millions		12 Months Ended
		Jan. 01, 2022		Jan. 02, 2021		Dec. 28, 2019
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Accumulated other comprehensive income (loss), Beginning balance		$ (130.6)		$ (102.1)
Other comprehensive income (loss) before reclassifications	[1]	17.2		(36.8)
Amounts reclassified from accumulated other comprehensive income (loss)		18.9		10.1
Reclassification from Accumulated Other Comprehensive Income, Current Period, Tax		(4.4)		(1.8)
Net reclassifications		14.5		8.3
Other comprehensive income (loss)		31.7	[1]	(28.5)	[1]	$ (13.8)
Accumulated other comprehensive income (loss), Ending Balance		(98.9)		(130.6)		(102.1)
Foreign currency translation adjustments [Member]
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Accumulated other comprehensive income (loss), Beginning balance		(36.8)		(47.6)
Other comprehensive income (loss) before reclassifications		(20.0)		10.8
Amounts reclassified from accumulated other comprehensive income (loss)		0.0		0.0
Reclassification from Accumulated Other Comprehensive Income, Current Period, Tax		0.0		0.0
Net reclassifications		0.0		0.0
Other comprehensive income (loss)	[1]	(20.0)		10.8
Accumulated other comprehensive income (loss), Ending Balance		(56.8)		(36.8)		(47.6)
Derivative [Member]
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Accumulated other comprehensive income (loss), Beginning balance		(20.3)		(5.8)
Other comprehensive income (loss) before reclassifications		7.7		(17.6)
Amounts reclassified from accumulated other comprehensive income (loss)	[2]	5.1		3.5
Reclassification from Accumulated Other Comprehensive Income, Current Period, Tax		(1.4)		(0.4)
Net reclassifications		3.7		3.1
Other comprehensive income (loss)	[1]	11.4		(14.5)
Accumulated other comprehensive income (loss), Ending Balance		(8.9)		(20.3)		(5.8)
Pension adjustments [Member]
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Accumulated other comprehensive income (loss), Beginning balance		(73.5)		(48.7)
Other comprehensive income (loss) before reclassifications		29.5		(30.0)
Amounts reclassified from accumulated other comprehensive income (loss)	[3]	13.8		6.6
Reclassification from Accumulated Other Comprehensive Income, Current Period, Tax		(3.0)		(1.4)
Net reclassifications		10.8		5.2
Other comprehensive income (loss)	[1]	40.3		(24.8)
Accumulated other comprehensive income (loss), Ending Balance		$ (33.2)		$ (73.5)		$ (48.7)

[1] Other comprehensive income (loss) is reported net of taxes and noncontrolling interest.

[2] Amounts related to foreign currency derivatives deemed to be highly effective are included in cost of goods sold. Amounts related to foreign currency derivatives that are no longer deemed to be highly effective are included in other income. Amounts related to interest rate swaps and the cross currency swap are included in interest expense.

[3] Amounts reclassified are included in the computation of net pension expense.