Restructuring and Other Charges - Narrative (Details) $ in Thousands				3 Months Ended			12 Months Ended			18 Months Ended
	Sep. 08, 2021	Dec. 23, 2019 USD ($) office	Dec. 29, 2018 USD ($) Employee	Dec. 29, 2019 USD ($)	Sep. 29, 2019 USD ($)	Dec. 30, 2018 USD ($)	Jan. 02, 2022 USD ($)	Jan. 03, 2021 USD ($)	Dec. 29, 2019 USD ($)	Jan. 01, 2023 USD ($)
Restructuring Activities [Line Items]
Restructuring, asset impairment and other charges							$ 3,621	$ (4,626)	$ 12,947
Restructuring reserve				$ 11,445		$ 11,907	2,354	1,064	11,445
Other write-off		$ 5,000
Restructuring charges								(4,626)	7,944
Operating Segments | AMS
Restructuring Activities [Line Items]
Restructuring, asset impairment and other charges							(1)	(288)	2,590
Other write-off		2,800
Operating Segments | EAAA
Restructuring Activities [Line Items]
Restructuring, asset impairment and other charges							3,622	(4,338)	10,357
Other write-off		$ 2,200
2021 Restructuring Plan
Restructuring Activities [Line Items]
Number of employees eliminated	188
Restructuring, expected savings							1,700
2021 Restructuring Plan | Minimum
Restructuring Activities [Line Items]
Future cash expenditures for restructuring							3,000
2021 Restructuring Plan | Maximum
Restructuring Activities [Line Items]
Future cash expenditures for restructuring							4,000
2021 Restructuring Plan | Operating Segments | EAAA
Restructuring Activities [Line Items]
Restructuring, asset impairment and other charges							3,900
2021 Restructuring Plan | Operating Segments | EAAA | Minimum
Restructuring Activities [Line Items]
Restructuring, asset impairment and other charges							4,000
2021 Restructuring Plan | Operating Segments | EAAA | Maximum
Restructuring Activities [Line Items]
Restructuring, asset impairment and other charges							5,000
2021 Restructuring Plan | Employee Severance
Restructuring Activities [Line Items]
Restructuring, asset impairment and other charges							2,257
Restructuring reserve				0		0	2,257	0	0
Restructuring charges								0	0
2021 Restructuring Plan | Employee Severance | Operating Segments | EAAA
Restructuring Activities [Line Items]
Restructuring, asset impairment and other charges							2,200
2021 Restructuring Plan | Deferred Bonus | Subsequent Event | Operating Segments | EAAA
Restructuring Activities [Line Items]
Restructuring, asset impairment and other charges										$ 500
2021 Restructuring Plan | Asset Impairment
Restructuring Activities [Line Items]
Restructuring, asset impairment and other charges							1,650
2021 Restructuring Plan | Asset Impairment | Subsequent Event | Operating Segments | EAAA
Restructuring Activities [Line Items]
Restructuring, asset impairment and other charges										$ 2,000
2019 Restructuring Plan
Restructuring Activities [Line Items]
Number of employees eliminated		105
Number of offices | office		2
Restructuring charges				9,000
Future cash expenditures for restructuring							9,000
Restructuring, expected savings							6,000
2019 Restructuring Plan | Operating Segments | AMS
Restructuring Activities [Line Items]
Restructuring charges				1,100
Cumulative restructuring and other charges incurred to date							800
2019 Restructuring Plan | Operating Segments | EAAA
Restructuring Activities [Line Items]
Restructuring charges				7,900
Cumulative restructuring and other charges incurred to date							4,200
2019 Restructuring Plan | Employee Severance
Restructuring Activities [Line Items]
Restructuring, asset impairment and other charges							(286)
Adjustment to previously recorded severance expense							(300)	(3,700)
Restructuring reserve				8,634		0	97	1,064	8,634
Restructuring charges				8,800				(3,704)	8,827
2019 Restructuring Plan | Other Exit Costs
Restructuring Activities [Line Items]
Restructuring, asset impairment and other charges							0
Restructuring reserve				139		0	0	0	139
Restructuring charges				200				0	188
2018 Restructuring Plan
Restructuring Activities [Line Items]
Restructuring, asset impairment and other charges						20,500
Adjustment to previously recorded severance expense								(900)
Number of employees eliminated | Employee			200
Asset impairment charges						8,600
Future cash expenditures for restructuring			$ 12,000
2018 Restructuring Plan | Operating Segments | AMS
Restructuring Activities [Line Items]
Restructuring, asset impairment and other charges						7,700
Cumulative restructuring and other charges incurred to date							6,400
2018 Restructuring Plan | Operating Segments | EAAA
Restructuring Activities [Line Items]
Restructuring, asset impairment and other charges						12,800
Cumulative restructuring and other charges incurred to date							12,100
2018 Restructuring Plan | Employee Severance
Restructuring Activities [Line Items]
Restructuring, asset impairment and other charges							0
Adjustment to previously recorded severance expense				(1,700)
Restructuring reserve				1,898		10,763	0	0	1,898
Restructuring charges						10,800		(223)	(1,743)
Future cash expenditures for restructuring			$ 10,800
2018 Restructuring Plan | Other Exit Costs
Restructuring Activities [Line Items]
Restructuring, asset impairment and other charges							0
Restructuring reserve				$ 774		1,144	$ 0	0	774
Restructuring charges					$ (700)	$ 1,100		$ (699)	$ 672