Acquisitions and Disposition - Acquisitions Narrative (Details) - USD ($) $ in Millions				3 Months Ended							12 Months Ended
	May 02, 2022	Mar. 07, 2022	Apr. 05, 2021	Jul. 02, 2023	Jan. 01, 2023	Oct. 02, 2022	Jan. 02, 2022	Oct. 03, 2021	Jul. 04, 2021	Apr. 04, 2021	Dec. 31, 2023	Jan. 01, 2023	Jan. 02, 2022
Business Acquisition [Line Items]
Goodwill impairment charge					$ 10.3	$ 30.7					$ 0.0	$ 41.0	$ 0.0
Gain on insurance settlement											0.0	0.0	19.0
Pediatric Therapeutic Services
Business Acquisition [Line Items]
Ownership percentage acquired (percent)	100.00%
Purchase price of acquisition	$ 82.1
Purchase price paid at closing	85.7
Additional consideration payable	1.1
Employee retention credits				$ 1.0		$ 0.1
Intangible assets acquired	40.3
Pro forma information, revenue of acquiree since acquisition date, actual											52.3	28.5
Pro forma information, earnings or loss of acquiree since acquisition date, actual											7.7	3.8
Pediatric Therapeutic Services | Customer relationships
Business Acquisition [Line Items]
Intangible assets acquired	$ 29.8
Acquired finite-lived intangible assets, weighted average useful life (years)	15 years
Pediatric Therapeutic Services | Trade names
Business Acquisition [Line Items]
Intangible assets acquired	$ 9.3
Acquired finite-lived intangible assets, weighted average useful life (years)	15 years
Pediatric Therapeutic Services | Non-compete agreements
Business Acquisition [Line Items]
Intangible assets acquired	$ 1.2
Acquired finite-lived intangible assets, weighted average useful life (years)	5 years
RocketPower
Business Acquisition [Line Items]
Ownership percentage acquired (percent)		100.00%
Purchase price of acquisition		$ 59.3
Purchase price paid at closing		61.8
Additional consideration payable		1.1
Intangible assets acquired		15.8
Pro forma information, revenue of acquiree since acquisition date, actual											7.1	24.3
Pro forma information, earnings or loss of acquiree since acquisition date, actual											(5.3)	(43.5)
Contingent consideration, liability		0.6
Possible future contingent consideration		31.8
Goodwill expected to be deductible											$ 27.3
Goodwill impairment charge												$ 41.0
RocketPower | Customer relationships
Business Acquisition [Line Items]
Intangible assets acquired		$ 7.5
Acquired finite-lived intangible assets, weighted average useful life (years)		3 years
RocketPower | Trade names
Business Acquisition [Line Items]
Intangible assets acquired		$ 6.6
Acquired finite-lived intangible assets, weighted average useful life (years)		10 years
RocketPower | Non-compete agreements
Business Acquisition [Line Items]
Intangible assets acquired		$ 1.7
Acquired finite-lived intangible assets, weighted average useful life (years)		6 years
Softworld, Inc.
Business Acquisition [Line Items]
Ownership percentage acquired (percent)			100.00%
Purchase price of acquisition			$ 215.0
Purchase price paid at closing			220.4
Additional consideration payable			2.6
Intangible assets acquired			79.4
Pro forma information, revenue of acquiree since acquisition date, actual													98.0
Pro forma information, earnings or loss of acquiree since acquisition date, actual													$ 4.7
Net working capital adjustment			(6.0)					$ (6.0)
Gain on insurance settlement							$ 19.0
Amortization of intangible assets							$ 2.0	$ 2.0	$ 2.0	$ 2.0
Softworld, Inc. | Customer relationships
Business Acquisition [Line Items]
Intangible assets acquired			$ 54.9
Acquired finite-lived intangible assets, weighted average useful life (years)			10 years
Softworld, Inc. | Trade names
Business Acquisition [Line Items]
Intangible assets acquired			$ 23.1
Acquired finite-lived intangible assets, weighted average useful life (years)			10 years
Softworld, Inc. | Non-compete agreements
Business Acquisition [Line Items]
Intangible assets acquired			$ 1.4
Acquired finite-lived intangible assets, weighted average useful life (years)			5 years