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Stock-Based Compensation and Other Stock Plans - Narrative (Details) - USD ($)
$ in Millions
12 Months Ended
Jan. 01, 2022
Jan. 02, 2021
Dec. 28, 2019
Share-based Compensation Arrangement by Share-based Payment Award, Compensation Cost [Line Items]      
Net stock-based compensation expense $ 41.4 $ 19.5 $ 23.8
Cash received from stock purchase and option plan exercises 162.4 55.8 51.4
Tax benefit realized from exercise and vesting of share-based payment arrangements $ 18.2 $ 8.2 $ 9.6
2011 Incentive Stock and Awards Plan      
Share-based Compensation Arrangement by Share-based Payment Award, Compensation Cost [Line Items]      
Number of shares available for future grants (in shares) 3,643,845