Segment Information (Details) $ in Millions	3 Months Ended		6 Months Ended
	Jul. 03, 2022 USD ($)	Jun. 27, 2021 USD ($)	Jul. 03, 2022 USD ($) segment	Jun. 27, 2021 USD ($)	Jan. 02, 2022 USD ($)
Segment Reporting [Abstract]
Number of operating segments | segment			2
Number of reportable segments | segment			2
Segment Information
Revenues	$ 520.3	$ 445.1	$ 1,077.9	$ 868.6
Operating expenses:
Selling, general and administrative	47.5	43.7	101.8	87.1
Depreciation and amortization	26.6	20.5	52.7	40.3
Total operating expenses	412.4	313.4	849.2	627.4
Operating profit	107.9	131.7	228.7	241.2
Interest expense, net	11.5	21.9	22.7	34.9
Other expense, net	3.6	(0.3)	5.2	(0.7)
Intercompany (income) expense	0.0	0.0	0.0	0.0
Income before income taxes	92.8	110.1	200.8	207.0
Income taxes	10.1	27.2	36.6	51.6
Net income	82.7	82.9	164.2	155.4
Total assets	3,125.6	2,672.7	3,125.6	2,672.7	$ 3,154.3
Service revenues
Segment Information
Revenues	416.6	382.5	851.6	742.9
Operating expenses:
Cost of service and vehicle sales	242.7	197.6	495.0	394.0
Vehicle and parts sales
Segment Information
Revenues	103.7	62.6	226.3	125.7
Operating expenses:
Cost of service and vehicle sales	95.6	51.6	199.7	106.0
United States
Segment Information
Revenues	418.5	393.0	857.3	751.3
Operating expenses:
Selling, general and administrative	42.3	40.5	89.5	81.0
Depreciation and amortization	21.5	18.4	42.2	36.3
Total operating expenses	314.8	268.3	641.7	525.8
Operating profit	103.7	124.7	215.6	225.5
Interest expense, net	11.5	22.0	22.7	35.0
Other expense, net	3.6	(0.1)	4.7	(0.3)
Intercompany (income) expense	(2.2)	(2.1)	(4.0)	(4.4)
Income before income taxes	90.8	104.9	192.2	195.2
Income taxes	9.6	25.5	33.9	48.2
Net income	81.2	79.4	158.3	147.0
Total assets	2,575.7	2,434.6	2,575.7	2,434.6
United States | Service revenues
Segment Information
Revenues	380.9	359.0	777.5	691.4
Operating expenses:
Cost of service and vehicle sales	211.8	182.7	433.5	360.8
United States | Vehicle and parts sales
Segment Information
Revenues	37.6	34.0	79.8	59.9
Operating expenses:
Cost of service and vehicle sales	39.2	26.7	76.5	47.7
International
Segment Information
Revenues	101.8	52.1	220.6	117.3
Operating expenses:
Selling, general and administrative	5.2	3.2	12.3	6.1
Depreciation and amortization	5.1	2.1	10.5	4.0
Total operating expenses	97.6	45.1	207.5	101.6
Operating profit	4.2	7.0	13.1	15.7
Interest expense, net	0.0	(0.1)	0.0	(0.1)
Other expense, net	0.0	(0.2)	0.5	(0.4)
Intercompany (income) expense	2.2	2.1	4.0	4.4
Income before income taxes	2.0	5.2	8.6	11.8
Income taxes	0.5	1.7	2.7	3.4
Net income	1.5	3.5	5.9	8.4
Total assets	549.9	238.1	549.9	238.1
International | Service revenues
Segment Information
Revenues	35.7	23.5	74.1	51.5
Operating expenses:
Cost of service and vehicle sales	30.9	14.9	61.5	33.2
International | Vehicle and parts sales
Segment Information
Revenues	66.1	28.6	146.5	65.8
Operating expenses:
Cost of service and vehicle sales	$ 56.4	$ 24.9	$ 123.2	$ 58.3