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Retirement Benefits - Narrative (Details) - USD ($) $ in Millions	12 Months Ended
	Jan. 01, 2023	Jan. 02, 2022	Jan. 03, 2021
Retirement Benefits [Abstract]
Liability for nonqualified plans	$ 196.6	$ 237.2
Earnings (loss) included in SG&A expenses	(36.3)	27.0	$ 23.0
Life insurance cash surrender value	194.3	232.9
Proceeds from company-owned life insurance	1.5	12.2	2.3
Tax-free earnings (loss) included in SG&A expenses	(36.0)	26.0	23.1
Net expense for retirement benefits	9.4	10.0	3.2
Benefit obligation	10.4	16.0
Fair value of plan assets	7.5	10.9
Unfunded liability	(2.9)	(5.1)
Pension expense	$ 0.4	$ 0.5	$ 0.6

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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 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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