Segment Information (Details) $ in Millions	3 Months Ended		9 Months Ended
	Oct. 02, 2022 USD ($)	Sep. 26, 2021 USD ($)	Oct. 02, 2022 USD ($) segment	Sep. 26, 2021 USD ($)	Jan. 02, 2022 USD ($)
Segment Reporting [Abstract]
Number of operating segments | segment			2
Number of reportable segments | segment			2
Segment Information
Revenues	$ 497.5	$ 420.7	$ 1,575.4	$ 1,289.3
Operating expenses:
Selling, general and administrative	51.0	49.8	152.8	136.9
Depreciation and amortization	25.2	21.2	77.9	61.5
Total operating expenses	413.5	323.9	1,262.7	951.3
Operating profit	84.0	96.8	312.7	338.0
Interest expense (income), net	13.3	11.1	36.0	46.0
Other expense (income), net	3.0	0.2	8.2	(0.5)
Intercompany (income) expense	0.0	0.0	0.0	0.0
Income before income taxes	67.7	85.5	268.5	292.5
Income taxes	17.4	19.8	54.0	71.4
Net income	50.3	65.7	214.5	221.1
Total assets	3,181.4	2,812.7	3,181.4	2,812.7	$ 3,154.3
Service revenues
Segment Information
Revenues	397.9	359.0	1,249.5	1,101.9
Operating expenses:
Cost of service and vehicle sales	244.0	198.4	739.0	592.4
Vehicle and parts sales
Segment Information
Revenues	99.6	61.7	325.9	187.4
Operating expenses:
Cost of service and vehicle sales	93.3	54.5	293.0	160.5
United States
Segment Information
Revenues	405.9	369.1	1,263.2	1,120.4
Operating expenses:
Selling, general and administrative	45.8	46.4	135.3	127.4
Depreciation and amortization	20.3	19.1	62.5	55.4
Total operating expenses	322.5	278.4	964.2	804.2
Operating profit	83.4	90.7	299.0	316.2
Interest expense (income), net	13.6	11.1	36.3	46.1
Other expense (income), net	3.4	(0.2)	8.1	(0.5)
Intercompany (income) expense	(1.8)	(1.8)	(5.8)	(6.2)
Income before income taxes	68.2	81.6	260.4	276.8
Income taxes	16.8	19.0	50.7	67.2
Net income	51.4	62.6	209.7	209.6
Total assets	2,663.1	2,573.1	2,663.1	2,573.1
United States | Service revenues
Segment Information
Revenues	362.8	336.5	1,140.3	1,027.9
Operating expenses:
Cost of service and vehicle sales	215.1	183.7	648.6	544.5
United States | Vehicle and parts sales
Segment Information
Revenues	43.1	32.6	122.9	92.5
Operating expenses:
Cost of service and vehicle sales	41.3	29.2	117.8	76.9
International
Segment Information
Revenues	91.6	51.6	312.2	168.9
Operating expenses:
Selling, general and administrative	5.2	3.4	17.5	9.5
Depreciation and amortization	4.9	2.1	15.4	6.1
Total operating expenses	91.0	45.5	298.5	147.1
Operating profit	0.6	6.1	13.7	21.8
Interest expense (income), net	(0.3)	0.0	(0.3)	(0.1)
Other expense (income), net	(0.4)	0.4	0.1	0.0
Intercompany (income) expense	1.8	1.8	5.8	6.2
Income before income taxes	(0.5)	3.9	8.1	15.7
Income taxes	0.6	0.8	3.3	4.2
Net income	(1.1)	3.1	4.8	11.5
Total assets	518.3	239.6	518.3	239.6
International | Service revenues
Segment Information
Revenues	35.1	22.5	109.2	74.0
Operating expenses:
Cost of service and vehicle sales	28.9	14.7	90.4	47.9
International | Vehicle and parts sales
Segment Information
Revenues	56.5	29.1	203.0	94.9
Operating expenses:
Cost of service and vehicle sales	$ 52.0	$ 25.3	$ 175.2	$ 83.6