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Acquisitions and Disposition - Acquisitions Narrative (Details) - USD ($) $ in Millions |  |  |  |  | 3 Months Ended | 12 Months Ended
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Apr. 05, 2021 | Nov. 18, 2020 | Jan. 14, 2020 | Jan. 02, 2019 | Jan. 02, 2022 | Oct. 03, 2021 | Jul. 04, 2021 | Apr. 04, 2021 | Jan. 03, 2021 | Sep. 27, 2020 | Jun. 28, 2020 | Mar. 29, 2020 | Jan. 02, 2022 | Jan. 03, 2021 | Dec. 29, 2019
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Payment for contingent consideration liability, financing activities |  |  |  |  |  |  |  |  |  |  |  |  | $ 1.6 | $ 0.0 | $ 0.0
Gain on insurance settlement |  |  |  |  |  |  |  |  |  |  |  |  | 19.0 | 0.0 | 0.0
Softworld, Inc. |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Ownership percentage acquired (percent) | 100.00% |  |  |  |  |  |  |  |  |  |  |  |  |  |
Purchase price of acquisition | $ 215.0 |  |  |  |  |  |  |  |  |  |  |  |  |  |
Purchase price paid at closing | 220.4 |  |  |  |  |  |  |  |  |  |  |  |  |  |
Net working capital adjustment | (6.0) |  |  |  |  | $ (6.0) |  |  |  |  |  |  |  |  |
Intangible assets acquired | 79.4 |  |  |  |  |  |  |  |  |  |  |  |  |  |
Pro forma revenue |  |  |  |  | $ 4,940.9 |  |  |  | $ 4,626.5 |  |  |  |  |  |
Pro forma net income |  |  |  |  | 157.7 |  |  |  | (70.8) |  |  |  |  |  |
Amortization of intangible assets |  |  |  |  | 2.0 | 2.0 | $ 2.0 | $ 2.0 | $ 2.0 | $ 2.0 | $ 2.0 | $ 2.0 |  |  |
Additional consideration payable | 2.6 |  |  |  |  |  |  |  |  |  |  |  |  |  |
Gain on insurance settlement |  |  |  |  | $ 19.0 |  |  |  |  |  |  |  |  |  |
Pro forma information, revenue of acquiree since acquisition date, actual |  |  |  |  |  |  |  |  |  |  |  |  | 98.0 |  |
Pro forma information, earnings or loss of acquiree since acquisition date, actual |  |  |  |  |  |  |  |  |  |  |  |  | 4.7 |  |
Softworld, Inc. | Customer Relationships |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Intangible assets acquired | $ 54.9 |  |  |  |  |  |  |  |  |  |  |  |  |  |
Acquired finite-lived intangible assets, weighted average useful life (years) | 10 years |  |  |  |  |  |  |  |  |  |  |  |  |  |
Softworld, Inc. | Noncompete Agreements |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Intangible assets acquired | $ 1.4 |  |  |  |  |  |  |  |  |  |  |  |  |  |
Acquired finite-lived intangible assets, weighted average useful life (years) | 5 years |  |  |  |  |  |  |  |  |  |  |  |  |  |
Softworld, Inc. | Trade Names |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Intangible assets acquired | $ 23.1 |  |  |  |  |  |  |  |  |  |  |  |  |  |
Acquired finite-lived intangible assets, weighted average useful life (years) | 10 years |  |  |  |  |  |  |  |  |  |  |  |  |  |
Greenwood/Asher |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Ownership percentage acquired (percent) |  | 100.00% |  |  |  |  |  |  |  |  |  |  |  |  |
Purchase price of acquisition |  | $ 3.5 |  |  |  |  |  |  |  |  |  |  |  |  |
Purchase price paid at closing |  | 5.2 |  |  |  |  |  |  |  |  |  |  |  |  |
Contingent consideration, liability |  | 2.1 |  |  |  |  |  |  |  |  |  |  |  |  |
Intangible assets acquired |  | 1.9 |  |  |  |  |  |  |  |  |  |  |  |  |
Expense related to earnout liability |  |  |  |  |  |  |  |  |  |  |  |  | 2.5 |  |
Greenwood/Asher | Customer Relationships |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Intangible assets acquired |  | $ 1.3 |  |  |  |  |  |  |  |  |  |  |  |  |
Acquired finite-lived intangible assets, weighted average useful life (years) |  | 10 years |  |  |  |  |  |  |  |  |  |  |  |  |
Greenwood/Asher | Trade Names |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Intangible assets acquired |  | $ 0.6 |  |  |  |  |  |  |  |  |  |  |  |  |
Acquired finite-lived intangible assets, weighted average useful life (years) |  | 10 years |  |  |  |  |  |  |  |  |  |  |  |  |
Insight |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Ownership percentage acquired (percent) |  |  | 100.00% |  |  |  |  |  |  |  |  |  |  |  |
Purchase price of acquisition |  |  | $ 34.5 |  |  |  |  |  |  |  |  |  |  |  |
Purchase price paid at closing |  |  | 38.1 |  |  |  |  |  |  |  |  |  |  |  |
Contingent consideration, liability |  |  | 1.6 |  |  |  |  |  |  |  |  |  |  |  |
Intangible assets acquired |  |  | $ 10.6 |  |  |  |  |  |  |  |  |  |  |  |
Acquired finite-lived intangible assets, weighted average useful life (years) |  |  | 10 years |  |  |  |  |  |  |  |  |  |  |  |
Expense related to earnout liability |  |  |  |  |  |  | $ 0.1 |  |  |  |  |  | 0.1 | 0.1 |
Payment for contingent consideration liability, financing activities |  |  |  |  |  | 1.6 |  |  |  |  |  |  |  |  |
Payment for contingent consideration liability |  |  |  |  |  | $ 1.8 |  |  |  |  |  |  |  |  |
Payments for previous acquisition |  |  |  |  |  |  |  |  |  |  | $ 0.1 |  |  |  |
NextGen Global Resources LLC |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Ownership percentage acquired (percent) |  |  |  | 100.00% |  |  |  |  |  |  |  |  |  |  |
Purchase price of acquisition |  |  |  | $ 51.0 |  |  |  |  |  |  |  |  |  |  |
Purchase price paid at closing |  |  |  | $ 54.3 |  |  |  |  |  |  |  |  |  |  |
Pro forma revenue |  |  |  |  |  |  |  |  |  |  |  |  |  |  | 78.3
Pro forma net income |  |  |  |  |  |  |  |  |  |  |  |  |  |  | 4.5
Global Technology Associates, LLC |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Ownership percentage acquired (percent) |  |  |  | 100.00% |  |  |  |  |  |  |  |  |  |  |
Purchase price of acquisition |  |  |  | $ 34.0 |  |  |  |  |  |  |  |  |  |  |
Purchase price paid at closing |  |  |  | $ 35.7 |  |  |  |  |  |  |  |  |  |  |
Pro forma revenue |  |  |  |  |  |  |  |  |  |  |  |  |  |  | 62.8
Pro forma net income |  |  |  |  |  |  |  |  |  |  |  |  |  |  | $ 4.5
Acquisition-related Costs | Softworld, Inc. |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Business Acquisition [Line Items] |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Net income (loss) |  |  |  |  |  |  |  |  |  |  |  |  | $ 1.3 | $ (1.3) |

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