Financial Instruments and Fair Value Measurements (Narrative) (Details) $ in Millions	1 Months Ended	6 Months Ended		11 Months Ended	12 Months Ended
	Dec. 29, 2023 USD ($)	Dec. 30, 2022 USD ($)	Jun. 16, 2022 USD ($)	Nov. 14, 2023 USD ($)	Dec. 31, 2021 USD ($)	Nov. 21, 2023	Mar. 13, 2023 USD ($)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Unrealized Gain (Loss) on Investments	$ (13.5)	$ (9.2)	$ (22.2)	$ (10.1)	$ (4.7)
Restricted Cash and Investments, Current	40.8	20.6	113.0	47.0	24.0
Restricted Cash and Investments, Noncurrent	39.9	36.6	$ 36.4	39.7	$ 36.2
Derivative, Notional Amount							$ 860.0
Derivative, Interest Rate Cap, Premium				20.0
Unrealized Gain (Loss) on Interest Rate Cash Flow Hedges, Pretax, Accumulated Other Comprehensive Income (Loss)				5.7
Other Comprehensive Income (Loss), Net Investment Hedge, Gain (Loss), Reclassification, before Tax				0.7
Unrealized Gain (Loss) on Derivatives	8.4
London Interbank Offered Rate
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative, Cap Interest Rate							4.65%
Secured Overnight Financing Rate (SOFR) Overnight Index Swap Rate
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative, Cap Interest Rate							3.84%
Professional Fees Escrow Account
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Restricted cash	17.6			$ 24.0
Takeback Term Loans | Derivative Financial Instruments, Liabilities | Scenario 1
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative, Remaining Maturity				5 years
Takeback Term Loans | Derivative Financial Instruments, Liabilities | Scenario 1 | Measurement Input Probability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative, Remaining Maturity | pURE						0.2500
Takeback Term Loans | Derivative Financial Instruments, Liabilities | Scenario 2
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative, Remaining Maturity				5 years
Takeback Term Loans | Derivative Financial Instruments, Liabilities | Scenario 2 | Measurement Input Probability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative, Remaining Maturity | pURE						0.2500
Takeback Term Loans | Derivative Financial Instruments, Liabilities | Scenario 3
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative, Remaining Maturity				5 years
Takeback Term Loans | Derivative Financial Instruments, Liabilities | Scenario 3 | Measurement Input Probability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative, Remaining Maturity | pURE						0.0625
Fourteen Point Seven Five Percent Second-Out Takeback Notes
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Stated interest rate				14.75%
Fourteen Point Seven Five Percent Second-Out Takeback Notes | Derivative Financial Instruments, Liabilities | Scenario 1
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative, Remaining Maturity				5 years
Fourteen Point Seven Five Percent Second-Out Takeback Notes | Derivative Financial Instruments, Liabilities | Scenario 1 | Measurement Input Probability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative, Remaining Maturity | pURE						0.2500
Fourteen Point Seven Five Percent Second-Out Takeback Notes | Derivative Financial Instruments, Liabilities | Scenario 1 | Measurement Input Coupon Rate
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative, Remaining Maturity | pURE						0.1475
Fourteen Point Seven Five Percent Second-Out Takeback Notes | Derivative Financial Instruments, Liabilities | Scenario 2
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative, Remaining Maturity				5 years
Fourteen Point Seven Five Percent Second-Out Takeback Notes | Derivative Financial Instruments, Liabilities | Scenario 2 | Measurement Input Probability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative, Remaining Maturity | pURE						0.2500
Fourteen Point Seven Five Percent Second-Out Takeback Notes | Derivative Financial Instruments, Liabilities | Scenario 2 | Measurement Input Coupon Rate
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative, Remaining Maturity | pURE						0.1475
Fourteen Point Seven Five Percent Second-Out Takeback Notes | Derivative Financial Instruments, Liabilities | Scenario 3
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative, Remaining Maturity				5 years
Fourteen Point Seven Five Percent Second-Out Takeback Notes | Derivative Financial Instruments, Liabilities | Scenario 3 | Measurement Input Probability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative, Remaining Maturity | pURE						0.0625
Fourteen Point Seven Five Percent Second-Out Takeback Notes | Derivative Financial Instruments, Liabilities | Scenario 3 | Measurement Input Coupon Rate
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Derivative, Remaining Maturity | pURE						0.1475
Senior Notes | Five Point Five Percent Notes [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Stated interest rate			5.50%
Senior Notes | Five Point Six Two Five Percent Note
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Stated interest rate			5.625%
Carrying Value | Fair Value, Inputs, Level 1 [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Restricted cash	80.7	57.2
Carrying Value | Fair Value, Inputs, Level 3
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Cash surrender value of life insurance	45.3	46.7
Fair Value, Measurements, Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Fair value of contingent consideration upon acquisition	14.7	7.3		$ 15.0
Debt and equity securities held in rabbi trusts	43.3	36.6
Fair Value, Measurements, Recurring | Fair Value, Inputs, Level 1 [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Fair value of contingent consideration upon acquisition	0.0	0.0
Debt and equity securities held in rabbi trusts	29.1	24.8
Fair Value, Measurements, Recurring | Level 2
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Fair value of contingent consideration upon acquisition	0.0	0.0
Debt and equity securities held in rabbi trusts	14.2	11.8
Fair Value, Measurements, Recurring | Fair Value, Inputs, Level 3
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Fair value of contingent consideration upon acquisition	14.7	7.3
Debt and equity securities held in rabbi trusts	$ 0.0	$ 0.0