Revenue - Revenue by Country (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019
Disaggregation of Revenue [Line Items]
Revenue from services	$ 4,909.7	$ 4,516.0	$ 5,355.6
United States
Disaggregation of Revenue [Line Items]
Revenue from services	3,513.4	3,260.2	3,892.5
Canada
Disaggregation of Revenue [Line Items]
Revenue from services	155.0	122.5	136.1
Puerto Rico
Disaggregation of Revenue [Line Items]
Revenue from services	102.1	77.0	74.6
Mexico
Disaggregation of Revenue [Line Items]
Revenue from services	92.7	114.4	123.6
Brazil
Disaggregation of Revenue [Line Items]
Revenue from services	0.0	17.0	34.1
Total Americas Region
Disaggregation of Revenue [Line Items]
Revenue from services	3,863.2	3,591.1	4,260.9
France
Disaggregation of Revenue [Line Items]
Revenue from services	223.1	198.2	248.6
Switzerland
Disaggregation of Revenue [Line Items]
Revenue from services	222.2	200.4	200.7
Portugal
Disaggregation of Revenue [Line Items]
Revenue from services	158.2	141.7	179.8
Russia
Disaggregation of Revenue [Line Items]
Revenue from services	132.2	118.5	117.6
Italy
Disaggregation of Revenue [Line Items]
Revenue from services	74.2	58.2	75.9
United Kingdom
Disaggregation of Revenue [Line Items]
Revenue from services	68.3	73.7	103.1
Germany
Disaggregation of Revenue [Line Items]
Revenue from services	34.0	30.1	41.6
Ireland
Disaggregation of Revenue [Line Items]
Revenue from services	26.8	19.9	33.1
Other
Disaggregation of Revenue [Line Items]
Revenue from services	68.0	54.6	67.5
Total Europe Region
Disaggregation of Revenue [Line Items]
Revenue from services	1,007.0	895.3	1,067.9
Total Asia-Pacific Region
Disaggregation of Revenue [Line Items]
Revenue from services	$ 39.5	$ 29.6	$ 26.8