Segment Information - Reconciliation of Segment AOI (Details) - USD ($) $ in Thousands	12 Months Ended
	Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Operating income (loss)	$ 104,797	$ (39,287)	$ 130,903
Interest expense	29,681	29,244	25,656
Other expense	2,483	10,889	3,431
Income (loss) before income tax expense	72,633	(79,420)	101,816
Amortization of acquired intangible assets	5,636	5,457	5,903
Goodwill and intangible asset impairment charge	0	121,258	0
Operating Segments | AMS
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Operating income (loss)	81,445	73,234	118,332
Amortization of acquired intangible assets	0	0	0
Goodwill and intangible asset impairment charge	0	2,695	0
Impact of change in equity award forfeiture accounting	0	757	0
Restructuring, asset impairment, severance and other charges	3,569	9,722	2,589
SEC fine	0	2,689	0
AOI	85,014	89,097	120,921
Operating Segments | EAAA
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]
Operating income (loss)	23,352	(112,521)	12,571
Amortization of acquired intangible assets	5,636	5,457	5,903
Goodwill and intangible asset impairment charge	0	118,563	0
Impact of change in equity award forfeiture accounting	0	650	0
Restructuring, asset impairment, severance and other charges	8,280	6,943	10,358
SEC fine	0	2,311	0
AOI	$ 37,268	$ 21,403	$ 28,832