Schedule II - Valuation Reserves (Details) - Valuation Reserves - USD ($) $ in Millions	12 Months Ended
	Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019
Allowance for doubtful accounts
SEC Schedule, 12-09, Movement in Valuation Allowances and Reserves [Roll Forward]
Balance at beginning of year		$ 12.9	$ 13.2
Charged to costs and expenses			3.4
Charged to other accounts			0.7
Currency exchange effects			0.0
Deductions from reserves			(4.4)
Balance at end of year			12.9
Deferred tax assets valuation allowance
SEC Schedule, 12-09, Movement in Valuation Allowances and Reserves [Roll Forward]
Balance at beginning of year	$ 20.2	19.0	27.8
Charged to costs and expenses	0.5	3.7	6.1
Charged to other accounts	0.0	0.0	0.0
Currency exchange effects	(0.8)	0.5	(0.3)
Deductions from reserves	(0.9)	(3.0)	(14.6)
Balance at end of year	$ 19.0	$ 20.2	$ 19.0