CONSOLIDATED STATEMENTS OF CASH FLOWS - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2023	Jan. 01, 2023	Jan. 02, 2022	Jan. 03, 2021
Operating Activities
Net income (loss) including noncontrolling interest	$ 886.6	$ 788.9	$ 445.3
Adjustments to reconcile net income (loss) including noncontrolling interest to net cash provided by (used in) operating activities:
Depreciation and amortization	316.4	332.2	371.8
Stock-based compensation	32.3	31.5	33.9
Bridge financing and debt extinguishment (income) expense	(1.6)	(10.6)	30.5
Changes in operating assets and liabilities, net of businesses acquired:
Accounts receivable and unbilled receivables	(21.7)	(87.9)	(158.9)
Inventories	(14.3)	(155.2)	7.0
Prepaid expenses and other assets	(42.6)	(50.4)	11.8
Accounts payable	(124.9)	45.9	99.1
Accrued expenses and other liabilities	49.7	(344.2)	(5.7)
Deferred taxes and income taxes receivable (payable), net	(230.9)	(35.2)	(21.4)
Other, net	(12.9)	(28.2)	11.2
Net cash provided by (used in) operating activities	836.1	486.8	824.6
Investing Activities
Purchases of property, plant and equipment	(114.9)	(92.6)	(101.6)
Purchase of businesses and other investments, net of cash acquired	(77.7)	(99.6)	(3,723.3)
Other, net	2.3	16.8	0.6
Net cash provided by (used in) investing activities	(190.3)	(175.4)	(3,824.3)
Financing Activities
Net proceeds (repayments) from credit facility	(125.0)	0.0	0.0
Proceeds from issuance of term loans and senior notes, net	0.0	0.0	3,975.9
Payments on other debt	(553.9)	(174.8)	(1,141.7)
Liquidations (maturities) of cross currency swap	(13.5)	43.1	0.0
Proceeds from stock options exercised	45.4	23.6	25.4
Payments for bridge financing and debt extinguishment	0.0	0.0	(30.5)	$ (30.5)
Other, net	(4.5)	(1.9)	(22.0)
Net cash provided by (used in) financing activities	(651.5)	(110.0)	2,807.1
Effect of exchange rate changes on cash and cash equivalents	15.9	(38.0)	(5.8)
Change in cash and cash equivalents	10.2	163.4	(198.4)
Cash and cash equivalents—beginning of period	638.1	474.7	673.1
Cash and cash equivalents—end of period	$ 648.3	$ 638.1	$ 474.7	$ 673.1