Pension Plans and Postretirement Benefits - Schedule of Fair Value of Assets Category (Details) - Recurring - Pension Plan - USD ($) $ in Millions	Jan. 01, 2023	Jan. 02, 2022
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	$ 507.0	$ 606.0
Level 1
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	228.7	245.2
Level 2
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	278.3	360.8
Level 3
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	0.0	0.0
Investments measured at net asset value:
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	247.7	311.2
Cash and Cash Equivalents
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	48.3	69.0
Cash and Cash Equivalents | Level 1
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	0.0	0.0
Cash and Cash Equivalents | Level 2
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	48.3	69.0
Cash and Cash Equivalents | Level 3
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	0.0	0.0
Equity securities
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	188.5	232.4
Equity securities | Level 1
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	2.8	2.4
Equity securities | Level 2
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	185.7	230.0
Equity securities | Level 3
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	0.0	0.0
U.S. government securities and futures
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	237.1	255.8
U.S. government securities and futures | Level 1
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	225.9	242.8
U.S. government securities and futures | Level 2
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	11.2	13.0
U.S. government securities and futures | Level 3
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	0.0	0.0
Corporate bonds
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	22.4	33.3
Corporate bonds | Level 1
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	0.0	0.0
Corporate bonds | Level 2
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	22.4	33.3
Corporate bonds | Level 3
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	0.0	0.0
Insurance contracts related to foreign plans
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	10.7	15.5
Insurance contracts related to foreign plans | Level 1
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	0.0	0.0
Insurance contracts related to foreign plans | Level 2
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	10.7	15.5
Insurance contracts related to foreign plans | Level 3
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	0.0	0.0
Alternatives | Investments measured at net asset value:
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	177.5	211.8
Mutual funds | Investments measured at net asset value:
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	4.3	7.3
Mortgage-backed securities | Investments measured at net asset value:
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	53.6	54.7
High-yield bonds | Investments measured at net asset value:
Defined Benefit Plan Disclosure [Line Items]
Fair value of plan assets	$ 12.3	$ 37.4