BUSINESS SEGMENTS - Segment Operating Income Results (Details) - USD ($) $ in Millions		3 Months Ended								12 Months Ended
		Jan. 03, 2020	Sep. 27, 2019	Jun. 28, 2019	Mar. 29, 2019	Dec. 28, 2018	Sep. 28, 2018	Jun. 29, 2018	Mar. 30, 2018	Jan. 03, 2020	Dec. 28, 2018	Dec. 29, 2017
Segment Reporting Information [Line Items]
Amortization of intangible assets										$ (35.0)	$ (37.3)	$ (36.1)
Merger costs											(2.6)
Restructuring charge											(10.1)
CEO retirement agreement expense										(20.0)	(18.9)	(18.1)
Impairment of intangible assets										0.0	0.0	(5.7)
Network and Security Solutions [Member]
Segment Reporting Information [Line Items]
Amortization of intangible assets										(16.4)	(17.0)	(14.4)
Electrical and Electronic Solutions [Member]
Segment Reporting Information [Line Items]
Amortization of intangible assets										(5.4)	(7.0)	(8.4)
Utility Power Solutions [Member]
Segment Reporting Information [Line Items]
Amortization of intangible assets										(13.2)	(13.3)	(13.3)
Corporate [Member]
Segment Reporting Information [Line Items]
Amortization of intangible assets	[1]									0.0	0.0	0.0
Operating Income (Loss) [Member]
Segment Reporting Information [Line Items]
Amortization of intangible assets		$ (8.6)	$ (8.8)	$ (8.8)	$ (8.8)	$ (8.7)	$ (9.6)	$ (9.7)	$ (9.3)	(35.0)	(37.3)	(36.1)
Merger costs										(12.8)
Restructuring charge							(0.2)	(9.2)		0.0	(9.4)	0.0
Acquisition and integration costs					$ 0.3		0.3	2.3	0.3	(0.3)	2.9	2.3
CEO retirement agreement expense											(2.6)
U.K. facility relocation costs						$ (0.2)	$ (0.2)	$ (0.4)	$ (0.2)		(1.0)
Impairment of intangible assets												(5.7)
Items impacting operating expense and operating income										(47.5)	(53.2)	(44.1)
Operating Income (Loss) [Member] | Network and Security Solutions [Member]
Segment Reporting Information [Line Items]
Amortization of intangible assets										(16.4)	(17.0)	(14.4)
Merger costs										0.0
Restructuring charge										0.0	(2.1)	0.0
Acquisition and integration costs										0.0	2.6	0.0
CEO retirement agreement expense											0.0
U.K. facility relocation costs											(0.2)
Impairment of intangible assets												(5.7)
Items impacting operating expense and operating income										(16.4)	(21.9)	(20.1)
Operating Income (Loss) [Member] | Electrical and Electronic Solutions [Member]
Segment Reporting Information [Line Items]
Amortization of intangible assets										(5.4)	(7.0)	(8.4)
Merger costs										0.0
Restructuring charge										(0.5)	(1.3)	0.5
Acquisition and integration costs										0.0	0.0	0.0
CEO retirement agreement expense											0.0
U.K. facility relocation costs											(0.8)
Impairment of intangible assets												0.0
Items impacting operating expense and operating income										(5.9)	(9.1)	(7.9)
Operating Income (Loss) [Member] | Utility Power Solutions [Member]
Segment Reporting Information [Line Items]
Amortization of intangible assets										(13.2)	(13.3)	(13.3)
Merger costs										0.0
Restructuring charge										0.1	(0.7)	(0.1)
Acquisition and integration costs										0.0	0.0	0.0
CEO retirement agreement expense											0.0
U.K. facility relocation costs											0.0
Impairment of intangible assets												0.0
Items impacting operating expense and operating income										(13.1)	(14.0)	(13.4)
Operating Income (Loss) [Member] | Corporate [Member]
Segment Reporting Information [Line Items]
Amortization of intangible assets										0.0	0.0	0.0
Merger costs										(12.8)
Restructuring charge										0.4	(5.3)	(0.4)
Acquisition and integration costs										(0.3)	0.3	2.3
CEO retirement agreement expense											(2.6)
U.K. facility relocation costs											0.0
Impairment of intangible assets												0.0
Items impacting operating expense and operating income										$ (12.1)	$ (8.2)	$ (2.7)

[1] Corporate "Total assets" primarily consists of cash and cash equivalents, deferred tax assets, and corporate fixed assets. Total assets in 2019 include the impact of the Company's adoption of ASU 2016-02, Leases, which resulted in the recognition of right-of-use assets for all leases with terms of more than 12 months.