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Related party transactions - Transactions with Non-Gates Entities (Details) - Affiliated Entity - USD ($)
$ in Millions
3 Months Ended 6 Months Ended
Jul. 02, 2022
Jul. 03, 2021
Jul. 02, 2022
Jul. 03, 2021
Jan. 01, 2022
Related Party Transaction          
Sales $ 15.4 $ 16.9 $ 32.3 $ 33.5  
Purchases (4.4) $ (5.3) (9.9) $ (10.9)  
Receivables 6.2   6.2   $ 5.4
Payables $ (3.2)   $ (3.2)   $ (3.6)