Other Assets - Schedule of Other Assets (Details) - USD ($) $ in Millions	Jan. 02, 2022	Jan. 03, 2021	Dec. 29, 2019
Other Assets [Line Items]
Life insurance cash surrender value	$ 232.9	$ 220.3
Intangibles, net of accumulated amortization	122.0	55.6
Long-term hosted software	152.1	72.7
Long-term customer receivable	0.0	2.4
Noncurrent restricted cash	6.6	5.1	$ 5.0
Workers' compensation receivable	5.5	6.1
Other	8.2	23.2
Other assets	389.1	319.9
Intangible assets, accumulated amortization	30.1	17.1
Other Assets
Other Assets [Line Items]
Intangible assets, accumulated amortization	39.1	26.7
Long Term Hosted Software
Other Assets [Line Items]
Long-term hosted software	$ 13.9	$ 7.2

Other Assets [Line Items]

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Amount, after allowance for credit loss, of right to consideration from customer for product sold and service rendered in normal course of business, classified as noncurrent.

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

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Carrying amount as of the balance sheet date of amounts expected to be recovered under the terms of insurance contracts.

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Accumulated amount of amortization of assets, excluding financial assets and goodwill, lacking physical substance with a finite life.

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Amount before accumulated amortization of intangible assets, excluding goodwill.

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Sum of the carrying amounts of all intangible assets, excluding goodwill, as of the balance sheet date, net of accumulated amortization and impairment charges.

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Amount of other miscellaneous assets expected to be realized or consumed after one year or normal operating cycle, if longer.

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Amount of noncurrent assets classified as other.

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Amount of cash restricted as to withdrawal or usage, classified as noncurrent. Cash includes, but is not limited to, currency on hand, demand deposits with banks or financial institutions, and other accounts with general characteristics of demand deposits.

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