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Operating Segments and Geographic Information - Operating Segment Information (Details) - USD ($)
$ in Thousands
3 Months Ended 12 Months Ended
Dec. 31, 2018
Sep. 30, 2018
Jul. 01, 2018
Apr. 01, 2018
Dec. 31, 2017
Oct. 01, 2017
Jul. 02, 2017
Apr. 02, 2017
Dec. 31, 2018
Dec. 31, 2017
Dec. 31, 2016
Segment Reporting Information [Line Items]                      
Revenues $ 655,390 $ 655,774 $ 668,639 $ 605,565 $ 604,884 $ 621,745 $ 610,633 $ 551,381 $ 2,585,368 $ 2,388,643 $ 2,356,672
Depreciation expense                 47,600 45,600 47,200
Amortization of intangibles                 98,829 103,997 98,385
Severance, restructuring, and acquisition integration costs 11,600 $ 11,700 $ 24,900 $ 20,400 9,900 $ 16,700 $ 9,600 $ 6,600 68,613 42,790 31,140
Acquisition of property, plant and equipment                 97,847 64,261 53,974
Segment assets 3,779,321       3,840,613       3,779,321 3,840,613 3,806,803
Enterprise Solutions                      
Segment Reporting Information [Line Items]                      
Severance, restructuring, and acquisition integration costs                 57,563 29,043 18,561
Industrial Solutions                      
Segment Reporting Information [Line Items]                      
Severance, restructuring, and acquisition integration costs                 11,050 13,747 12,579
Reportable Segment                      
Segment Reporting Information [Line Items]                      
Revenues                 2,585,368 2,388,643 2,356,672
Segment EBITDA                 475,380 430,748 433,789
Depreciation expense                 47,615 45,597 47,208
Amortization of intangibles                 98,829 103,997 98,385
Amortization of software development intangible assets                 2,188 56 0
Severance, restructuring, and acquisition integration costs                 68,613 42,790 31,140
Purchase accounting effects of acquisitions                 3,497 6,133 (2,079)
Deferred Revenue Adjustments                 6,612 0 6,687
Acquisition of property, plant and equipment                 94,834 62,759 53,582
Segment assets 1,220,110       1,146,395       1,220,110 1,146,395 913,998
Reportable Segment | Enterprise Solutions                      
Segment Reporting Information [Line Items]                      
Segment EBITDA                 267,656 216,558 239,978
Depreciation expense                 28,861 26,272 29,455
Amortization of intangibles                 45,944 51,054 48,966
Amortization of software development intangible assets                 2,180 56 0
Severance, restructuring, and acquisition integration costs                 57,563 29,043 18,561
Purchase accounting effects of acquisitions                 3,497 6,133 (2,079)
Deferred Revenue Adjustments                 6,612 0 1,774
Acquisition of property, plant and equipment                 65,619 49,440 38,392
Segment assets 761,309       687,914       761,309 687,914 571,960
Reportable Segment | Industrial Solutions                      
Segment Reporting Information [Line Items]                      
Segment EBITDA                 207,724 214,190 193,811
Depreciation expense                 18,754 19,325 17,753
Amortization of intangibles                 52,885 52,943 49,419
Amortization of software development intangible assets                 8 0 0
Severance, restructuring, and acquisition integration costs                 11,050 13,747 12,579
Deferred Revenue Adjustments                 0 0 4,913
Acquisition of property, plant and equipment                 29,215 13,319 15,190
Segment assets $ 458,801       $ 458,481       458,801 458,481 342,038
Software Development | Reportable Segment                      
Segment Reporting Information [Line Items]                      
Amortization of intangibles                 2,188 56 0
Segment revenues | Reportable Segment                      
Segment Reporting Information [Line Items]                      
Revenues                 2,591,980 2,388,643 2,357,805
Segment revenues | Reportable Segment | Enterprise Solutions                      
Segment Reporting Information [Line Items]                      
Revenues                 1,522,178 1,356,305 1,372,941
Segment revenues | Reportable Segment | Industrial Solutions                      
Segment Reporting Information [Line Items]                      
Revenues                 1,069,802 1,032,338 984,864
Affiliate revenues | Reportable Segment                      
Segment Reporting Information [Line Items]                      
Revenues                 6,166 5,158 2,870
Affiliate revenues | Reportable Segment | Enterprise Solutions                      
Segment Reporting Information [Line Items]                      
Revenues                 6,085 5,091 2,799
Affiliate revenues | Reportable Segment | Industrial Solutions                      
Segment Reporting Information [Line Items]                      
Revenues                 81 67 71
Patent settlement | Reportable Segment                      
Segment Reporting Information [Line Items]                      
Revenues                 0 0 5,554
Patent settlement | Reportable Segment | Enterprise Solutions                      
Segment Reporting Information [Line Items]                      
Revenues                 $ 0 $ 0 $ 5,554