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Derivative Financial Instruments (Details) $ in Thousands, £ in Millions |  | 3 Months Ended | 12 Months Ended |  |  |  |  |
--- | --- | --- | --- | --- | --- | --- | --- | ---
Jan. 23, 2023 USD ($) | Jan. 01, 2023 USD ($) | Jan. 02, 2022 USD ($) | Sep. 30, 2018 agreement | Jan. 23, 2023 GBP (£) | Dec. 31, 2022 GBP (£) | Dec. 30, 2022 USD ($) | Dec. 28, 2022 USD ($) | Dec. 28, 2022 GBP (£) | Oct. 02, 2022 USD ($)
Derivative [Line Items] |  |  |  |  |  |  |  |  |  |
Gain on foreign currency forward contract |  | $ 67,995 | $ 0 |  |  |  |  |  |  |
Gains (losses) on cash flow hedges recognized in comprehensive income |  | (89) | $ 2,666 |  |  |  |  |  |  |
RPS Group PLC |  |  |  |  |  |  |  |  |  |
Derivative [Line Items] |  |  |  |  |  |  |  |  |  |
Derivative, forward exchange rate |  |  |  |  |  |  | 1.0852 | 1.086 | 1.086 |
Interest Rate Swap | Designated as cash flow hedges | Derivatives designated as hedging instruments |  |  |  |  |  |  |  |  |  |
Derivative [Line Items] |  |  |  |  |  |  |  |  |  |
Notional amount |  | $ 196,900 |  |  |  |  |  |  |  |
Number of derivative agreements | agreement |  |  |  | 5 |  |  |  |  |  |
Fixed rate |  | 2.79% |  |  |  |  |  |  |  |
Credit to be reclassified during next twelve months |  | $ 2,200 |  |  |  |  |  |  |  |
Interest Rate Swap | Designated as cash flow hedges | Derivatives designated as hedging instruments | Other current liabilities |  |  |  |  |  |  |  |  |  |
Derivative [Line Items] |  |  |  |  |  |  |  |  |  |
Fair value loss of interest rate swap agreements |  |  |  |  |  |  |  |  |  | $ 2,400
Interest Rate Swap | Designated as cash flow hedges | Derivatives designated as hedging instruments | Other Noncurrent Assets |  |  |  |  |  |  |  |  |  |
Derivative [Line Items] |  |  |  |  |  |  |  |  |  |
Fair value gain of interest rate swap agreements |  | 2,300 |  |  |  |  |  |  |  |
Interest Rate Swap 1 | Designated as cash flow hedges | Derivatives designated as hedging instruments |  |  |  |  |  |  |  |  |  |
Derivative [Line Items] |  |  |  |  |  |  |  |  |  |
Notional amount |  | 39,400 |  |  |  |  |  |  |  |
Interest Rate Swap 2 | Designated as cash flow hedges | Derivatives designated as hedging instruments |  |  |  |  |  |  |  |  |  |
Derivative [Line Items] |  |  |  |  |  |  |  |  |  |
Notional amount |  | 39,400 |  |  |  |  |  |  |  |
Interest Rate Swap 3 | Designated as cash flow hedges | Derivatives designated as hedging instruments |  |  |  |  |  |  |  |  |  |
Derivative [Line Items] |  |  |  |  |  |  |  |  |  |
Notional amount |  | 39,400 |  |  |  |  |  |  |  |
Interest Rate Swap 4 | Designated as cash flow hedges | Derivatives designated as hedging instruments |  |  |  |  |  |  |  |  |  |
Derivative [Line Items] |  |  |  |  |  |  |  |  |  |
Notional amount |  | 39,400 |  |  |  |  |  |  |  |
Interest Rate Swap 5 | Designated as cash flow hedges | Derivatives designated as hedging instruments |  |  |  |  |  |  |  |  |  |
Derivative [Line Items] |  |  |  |  |  |  |  |  |  |
Notional amount |  | 39,400 |  |  |  |  |  |  |  |
Foreign Exchange Forward | RPS Group PLC |  |  |  |  |  |  |  |  |  |
Derivative [Line Items] |  |  |  |  |  |  |  |  |  |
Notional amount |  |  |  |  |  | £ 714.0 | $ 774,800 | $ 775,400 | £ 714.0 |
Foreign currency forward contract, asset fair value |  | 87,900 |  |  |  |  |  |  |  | $ 19,900
Gain on foreign currency forward contract |  | $ 68,000 |  |  |  |  |  |  |  |
Foreign Exchange Forward | RPS Group PLC | Subsequent Event |  |  |  |  |  |  |  |  |  |
Derivative [Line Items] |  |  |  |  |  |  |  |  |  |
Notional amount | £ |  |  |  |  | £ 714.0 |  |  |  |  |
Gain on foreign currency forward contract | $ 109,000 |  |  |  |  |  |  |  |  |

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