Reportable Segments - Summarized Financial Information (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2022	Jan. 01, 2022	Jan. 02, 2021
Segment Reporting, Revenue Reconciling Item [Line Items]
Gross revenues	$ 786,778	$ 706,706	$ 659,296
Segment income before taxes	62,374	62,105	28,968
Amortization expense	32,341	33,498	34,596
Assets	935,723	961,943
INF
Segment Reporting, Revenue Reconciling Item [Line Items]
Gross revenues	395,878	383,725	352,965
BTS
Segment Reporting, Revenue Reconciling Item [Line Items]
Gross revenues	232,577	185,995	157,432
GEO
Segment Reporting, Revenue Reconciling Item [Line Items]
Gross revenues	158,323	136,986	148,899
Operating segments
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment income before taxes	154,709	140,086	113,678
Operating segments | INF
Segment Reporting, Revenue Reconciling Item [Line Items]
Gross revenues	395,878	383,725	352,965
Segment income before taxes	68,259	71,838	62,574
Assets	226,301	246,377
Operating segments | BTS
Segment Reporting, Revenue Reconciling Item [Line Items]
Gross revenues	232,577	185,995	157,432
Segment income before taxes	43,810	35,221	21,091
Assets	231,049	246,841
Operating segments | GEO
Segment Reporting, Revenue Reconciling Item [Line Items]
Gross revenues	158,323	136,986	148,899
Segment income before taxes	42,640	33,027	30,013
Assets	366,385	361,793
Corporate
Segment Reporting, Revenue Reconciling Item [Line Items]
Segment income before taxes	(92,335)	(77,981)	$ (84,710)
Assets	$ 111,988	$ 106,932