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Revenue - Revenue by Country (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2023	Jan. 02, 2022	Jan. 03, 2021
Disaggregation of Revenue [Line Items]
Revenue from services	$ 4,965.4	$ 4,909.7	$ 4,516.0
United States
Disaggregation of Revenue [Line Items]
Revenue from services	3,671.5	3,513.4	3,260.2
Canada
Disaggregation of Revenue [Line Items]
Revenue from services	168.2	155.0	122.5
Puerto Rico
Disaggregation of Revenue [Line Items]
Revenue from services	112.4	102.1	77.0
Mexico
Disaggregation of Revenue [Line Items]
Revenue from services	46.5	92.7	114.4
Brazil
Disaggregation of Revenue [Line Items]
Revenue from services	0.0	0.0	17.0
Total Americas Region
Disaggregation of Revenue [Line Items]
Revenue from services	3,998.6	3,863.2	3,591.1
Switzerland
Disaggregation of Revenue [Line Items]
Revenue from services	222.8	222.2	200.4
France
Disaggregation of Revenue [Line Items]
Revenue from services	199.4	223.1	198.2
Portugal
Disaggregation of Revenue [Line Items]
Revenue from services	169.5	158.2	141.7
Italy
Disaggregation of Revenue [Line Items]
Revenue from services	69.3	74.2	58.2
Russia
Disaggregation of Revenue [Line Items]
Revenue from services	63.4	132.2	118.5
United Kingdom
Disaggregation of Revenue [Line Items]
Revenue from services	57.1	68.3	73.7
Other
Disaggregation of Revenue [Line Items]
Revenue from services	143.2	128.8	104.6
Total Europe Region
Disaggregation of Revenue [Line Items]
Revenue from services	924.7	1,007.0	895.3
Total Asia-Pacific Region
Disaggregation of Revenue [Line Items]
Revenue from services	$ 42.1	$ 39.5	$ 29.6

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