Stock-Based Compensation Additional Information (Detail) - USD ($) $ / shares in Units, $ in Millions	12 Months Ended
Dec. 31, 2022	Jan. 01, 2022	Jan. 02, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock-based compensation expense	$ 33.4	$ 38.1	$ 28.9
Income tax benefits for grants	$ 6.5	$ 7.5	$ 5.6
Maximum expiry period of options granted from the grant date	10 years
Vesting period of options granted	3 years
Lapsing period of restrictions related to restricted stock issued	three - to four- year
Weighted-average fair values for options granted	$ 8.46	$ 11.14	$ 8.20
Total pretax intrinsic value of options exercised	$ 0.4	$ 11.4	$ 9.3
Closing stock price	$ 10.93
Stock options exercisable and in-the-money, number		2,247,575
Stock options exercisable and in-the-money, weighted average exercise price		$ 21.70
Available For Issuance [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock incentive units	5,543,811
Option Or Stock Appreciation Right [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock incentive units	1.0
Non-Stock Option Awards [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock incentive units	2.6
Employee Stock Option [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Unrecognized compensation expense related to nonvested shares and stock option grants	$ 0.1	$ 0.2	$ 0.1
Weighted-average period of recognition	10 months 24 days	1 year 3 months 18 days	10 months 24 days
Restricted Awards [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Unrecognized compensation expense related to nonvested shares and stock option grants	$ 19.4	$ 19.8	$ 18.5
Weighted-average period of recognition	1 year 7 months 6 days	1 year 7 months 6 days	1 year 6 months
Total fair value of shares vested	$ 10.9	$ 34.8	$ 35.0
Performance Awards [Member]
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Unrecognized compensation expense related to nonvested shares and stock option grants	$ 10.8	$ 16.1	$ 1.4
Weighted-average period of recognition	1 year 7 months 6 days	1 year 4 months 24 days	1 year 4 months 24 days
Total fair value of shares vested	$ 9.3	$ 6.2	$ 28.0

Amount of cost not yet recognized for nonvested award under share-based payment arrangement.

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Weighted-average period over which cost not yet recognized is expected to be recognized for award under share-based payment arrangement, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

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Amount of tax benefit for recognition of expense of award under share-based payment arrangement.

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Amount of noncash expense for share-based payment arrangement.

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Fair value of share-based awards for which the grantee gained the right by satisfying service and performance requirements, to receive or retain shares or units, other instruments, or cash.

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Amount of accumulated difference between fair value of underlying shares on dates of exercise and exercise price on options exercised (or share units converted) into shares.

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The weighted average grant-date fair value of options granted during the reporting period as calculated by applying the disclosed option pricing methodology.

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