Intangible Assets, Net - Summary of Intangible Assets (Details) - USD ($) $ in Millions	Jan. 01, 2022	Jan. 02, 2021	Dec. 28, 2019
Not subject to amortization
Total intangible assets not subject to amortization	$ 459.9	$ 455.5
Subject to amortization
Intangibles subject to amortization Cost	943.2	907.1
Total intangible assets	1,403.1	1,362.6
Intangible assets - Accumulated Amortization	433.3	375.0
Total	509.9	532.1
Total intangible assets - Net	969.8	987.6	$ 597.0
Customer relationships
Subject to amortization
Intangibles subject to amortization Cost	831.4	809.5
Intangible assets - Accumulated Amortization	368.7	324.3
Total	462.7	485.2
Patents
Subject to amortization
Intangibles subject to amortization Cost	19.2	19.2
Intangible assets - Accumulated Amortization	8.7	6.4
Total	10.5	12.8
Software
Subject to amortization
Intangibles subject to amortization Cost	72.2	62.5
Intangible assets - Accumulated Amortization	48.5	38.2
Total	23.7	24.3
Other
Subject to amortization
Intangibles subject to amortization Cost	20.4	15.9
Intangible assets - Accumulated Amortization	7.4	6.1
Total	13.0	9.8
Trademarks
Not subject to amortization
Total intangible assets not subject to amortization	459.2	455.5
Intellectual Property
Not subject to amortization
Total intangible assets not subject to amortization	$ 0.7	$ 0.0