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Supplemental Balance Sheet Information - Other Long-term Liabilities (Details) - USD ($) $ in Millions	Jan. 01, 2023	Jan. 02, 2022
Organization, Consolidation and Presentation of Financial Statements [Abstract]
Unrecognized tax benefits, including accrued interest and penalties	$ 176.3	$ 150.7
Operating lease liabilities	125.9	138.0
Deferred compensation liabilities	92.2	115.5
Pension and postretirement related liabilities	50.2	67.2
Contract liabilities	20.2	25.3
Derivative liabilities	19.4	9.6
Warranty reserve	7.0	7.7
Other	56.0	71.0
Total other long-term liabilities	$ 547.2	$ 585.0
Operating Lease, Liability, Noncurrent, Statement of Financial Position [Extensible List]	Total other long-term liabilities	Total other long-term liabilities

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