Retirement Benefits - Narrative (Details) - USD ($) $ in Millions	12 Months Ended
Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019
Retirement Benefits [Abstract]
Liability for nonqualified plans	$ 237.2	$ 216.8
Earnings (loss) included in SG&A expenses	27.0	23.0	$ 32.5
Life insurance cash surrender value	232.9	220.3
Proceeds from company-owned life insurance	12.2	2.3	3.0
Tax-free earnings (loss) included in SG&A expenses	26.0	23.1	32.2
Net expense for retirement benefits	10.0	3.2	9.1
Benefit obligation	16.0	17.6
Fair value of plan assets	10.9	11.3
Unfunded liability	(5.1)	(6.3)
Pension expense	$ 0.5	$ 0.6	$ 0.3

Earnings (losses) on the value of the deferred compensation assets.

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The cost participants' earnings (losses) on the unqualified deferred compensation plan liability.

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Aggregate carrying value as of the balance sheet date of the liabilities for all deferred compensation arrangements. Represents currently earned compensation under compensation arrangements that is not actually paid until a later date.

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Carrying amount as of the balance sheet date of assets held under deferred compensation agreements.

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Amount of actuarial present value of benefits attributed to service rendered by employee for defined benefit plan.

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Amount of asset segregated and restricted to provide benefit under defined benefit plan. Asset includes, but is not limited to, stock, bond, other investment, earning from investment, and contribution by employer and employee.

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Amount of funded (unfunded) status of defined benefit plan, measured as difference between fair value of plan assets and benefit obligation. Includes, but is not limited to, overfunded (underfunded) status.

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Amount of net periodic benefit cost (credit) for defined benefit plan.

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Amount of cost for defined contribution plan.

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Amount of cash inflow for proceeds from settlement of corporate-owned life insurance policy, classified as investing activities. Includes, but is not limited to, bank-owned life insurance policy.

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