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Acquisitions and Disposition - Fair Value of Assets Assumed and Liabilities Acquired (Details) - USD ($) $ in Millions | May 02, 2022 | Mar. 07, 2022 | Apr. 05, 2021 | Jan. 01, 2023 | Jan. 02, 2022 | Jan. 03, 2021
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Business Acquisition [Line Items] |  |  |  |  |  |
Goodwill |  |  |  | $ 151.1 | $ 114.8 | $ 3.5
Softworld, Inc. |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |
Cash |  |  | $ 1.4 |  |  |
Trade accounts receivable |  |  | 21.6 |  |  |
Prepaid expenses and other current assets |  |  | 3.3 |  |  |
Net property and equipment |  |  | 1.2 |  |  |
Operating lease right-of-use assets |  |  | 7.6 |  |  |
Non-current deferred tax |  |  | 5.9 |  |  |
Goodwill |  |  | 111.3 |  |  |
Intangibles |  |  | 79.4 |  |  |
Other assets, noncurrent |  |  | 1.2 |  |  |
Accounts payable and accrued liabilities, current |  |  | (2.5) |  |  |
Operating lease liabilities, current |  |  | (1.3) |  |  |
Accrued payroll and related taxes, current |  |  | (4.6) |  |  |
Income and other taxes, current |  |  | (1.2) |  |  |
Operating lease liabilities, noncurrent |  |  | (6.3) |  |  |
Total consideration, including working capital adjustments |  |  | $ 217.0 |  |  |
Pediatric Therapeutic Services |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |
Cash | $ 0.9 |  |  |  |  |
Trade accounts receivable | 10.0 |  |  |  |  |
Prepaid expenses and other current assets | 1.6 |  |  |  |  |
Net property and equipment | 0.4 |  |  |  |  |
Goodwill | 36.3 |  |  |  |  |
Intangibles | 40.3 |  |  |  |  |
Accounts payable and accrued liabilities, current | (2.6) |  |  |  |  |
Accrued payroll and related taxes, current | (0.1) |  |  |  |  |
Total consideration, including working capital adjustments | $ 86.8 |  |  |  |  |
RocketPower |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |
Cash |  | $ 3.5 |  |  |  |
Trade accounts receivable |  | 6.9 |  |  |  |
Prepaid expenses and other current assets |  | 1.8 |  |  |  |
Net property and equipment |  | 0.1 |  |  |  |
Goodwill |  | 41.0 |  |  |  |
Intangibles |  | 15.8 |  |  |  |
Accounts payable and accrued liabilities, current |  | (2.9) |  |  |  |
Accrued payroll and related taxes, current |  | (1.5) |  |  |  |
Other long-term liabilities |  | (1.2) |  |  |  |
Total consideration, including working capital adjustments |  | $ 63.5 |  |  |  |

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