Acquisitions and Disposition - Acquisitions Narrative (Details) - USD ($) $ in Millions					3 Months Ended								12 Months Ended
	Apr. 05, 2021	Nov. 18, 2020	Jan. 14, 2020	Jan. 02, 2019	Jan. 02, 2022	Oct. 03, 2021	Jul. 04, 2021	Apr. 04, 2021	Jan. 03, 2021	Sep. 27, 2020	Jun. 28, 2020	Mar. 29, 2020	Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019
Business Acquisition [Line Items]
Payment for contingent consideration liability, financing activities													$ 1.6	$ 0.0	$ 0.0
Gain on insurance settlement													19.0	0.0	0.0
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
Net working capital adjustment	(6.0)					$ (6.0)
Intangible assets acquired	79.4
Pro forma revenue					$ 4,940.9				$ 4,626.5
Pro forma net income					157.7				(70.8)
Amortization of intangible assets					2.0	2.0	$ 2.0	$ 2.0	$ 2.0	$ 2.0	$ 2.0	$ 2.0
Additional consideration payable	2.6
Gain on insurance settlement					$ 19.0
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
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. | Noncompete Agreements
Business Acquisition [Line Items]
Intangible assets acquired	$ 1.4
Acquired finite-lived intangible assets, weighted average useful life (years)	5 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
Greenwood/Asher
Business Acquisition [Line Items]
Ownership percentage acquired (percent)		100.00%
Purchase price of acquisition		$ 3.5
Purchase price paid at closing		5.2
Contingent consideration, liability		2.1
Intangible assets acquired		1.9
Expense related to earnout liability													2.5
Greenwood/Asher | Customer Relationships
Business Acquisition [Line Items]
Intangible assets acquired		$ 1.3
Acquired finite-lived intangible assets, weighted average useful life (years)		10 years
Greenwood/Asher | Trade Names
Business Acquisition [Line Items]
Intangible assets acquired		$ 0.6
Acquired finite-lived intangible assets, weighted average useful life (years)		10 years
Insight
Business Acquisition [Line Items]
Ownership percentage acquired (percent)			100.00%
Purchase price of acquisition			$ 34.5
Purchase price paid at closing			38.1
Contingent consideration, liability			1.6
Intangible assets acquired			$ 10.6
Acquired finite-lived intangible assets, weighted average useful life (years)			10 years
Expense related to earnout liability							$ 0.1						0.1	0.1
Payment for contingent consideration liability, financing activities						1.6
Payment for contingent consideration liability						$ 1.8
Payments for previous acquisition											$ 0.1
NextGen Global Resources LLC
Business Acquisition [Line Items]
Ownership percentage acquired (percent)				100.00%
Purchase price of acquisition				$ 51.0
Purchase price paid at closing				$ 54.3
Pro forma revenue															78.3
Pro forma net income															4.5
Global Technology Associates, LLC
Business Acquisition [Line Items]
Ownership percentage acquired (percent)				100.00%
Purchase price of acquisition				$ 34.0
Purchase price paid at closing				$ 35.7
Pro forma revenue															62.8
Pro forma net income															$ 4.5
Acquisition-related Costs | Softworld, Inc.
Business Acquisition [Line Items]
Net income (loss)													$ 1.3	$ (1.3)