Goodwill and Intangible Assets - Rollforward (Details) - USD ($) $ in Millions	3 Months Ended		12 Months Ended
	Jan. 01, 2023	Oct. 02, 2022	Dec. 31, 2023	Jan. 01, 2023	Jan. 02, 2022
Goodwill [Roll Forward]
Goodwill, beginning balance			$ 151.1	$ 114.8
Additions to Goodwill			0.0	77.3
Goodwill impairment charge	$ (10.3)	$ (30.7)	0.0	(41.0)	$ 0.0
Goodwill, ending balance	151.1		151.1	151.1	114.8
Science, Engineering & Technology
Goodwill [Roll Forward]
Goodwill, beginning balance			111.3	111.3
Additions to Goodwill			0.0	0.0
Goodwill impairment charge			0.0	0.0
Goodwill, ending balance	111.3		111.3	111.3	111.3
Education
Goodwill [Roll Forward]
Goodwill, beginning balance			39.8	3.5
Additions to Goodwill			0.0	36.3
Goodwill impairment charge			0.0	0.0
Goodwill, ending balance	39.8		39.8	39.8	3.5
Outsourcing & Consulting
Goodwill [Roll Forward]
Goodwill, beginning balance	10.3		0.0	0.0
Additions to Goodwill			0.0	41.0
Goodwill impairment charge			0.0	(41.0)
Goodwill, ending balance	$ 0.0	$ 10.3	$ 0.0	$ 0.0	$ 0.0