Equity-Based Compensation - Stock Option Activity (Details) - Employee Stock Option [Member] - $ / shares	9 Months Ended	12 Months Ended
Oct. 01, 2023	Jan. 01, 2023
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding
Options Outstanding, Beginning balance	322,793
Options Outstanding, Forfeited	(161,396)
Options Outstanding, Ending balance	161,397	322,793
Options Outstanding, exercisable	161,397
Options Outstanding, Expected to vest	161,397
Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Exercise Price
Weighted-Average Exercise Price per Option, Beginning balance (in dollars per share)	$ 11.35
Weighted-Average Exercise Price per Option, Forfeited (in dollars per share)	(11.35)
Weighted-Average Exercise Price per Option, Ending balance (in dollars per share)	11.35	$ 11.35
Weighted-Average Exercise Price per Option, exercisable (in dollars per share)	11.35
Weighted-Average Exercise Price per Option, Expected to vest (in dollars per share)	$ 11.35
Share-based Compensation Arrangement by Share-based Payment Award, Options, Additional Disclosures
Weighted-Average Remaining Contractual Life (years)	7 years 6 months 14 days	8 years 3 months 14 days
Weighted-Average Remaining Contractual Life (years), Vested and exercisable	7 years 6 months 14 days
Weighted-Average Remaining Contractual Life (years), Expected to vest	7 years 6 months 14 days

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- Definition

The number of shares under options that were cancelled during the reporting period as a result of occurrence of a terminating event specified in contractual agreements pertaining to the stock option plan.

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- Definition

Number of options outstanding, including both vested and non-vested options.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(i)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480429/718-10-50-2

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
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-Section 50
-Paragraph 2
-Subparagraph (c)(1)(ii)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480429/718-10-50-2

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- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

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Weighted average price at which grantees can acquire the shares reserved for issuance under the stock option plan.

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- Definition

Number of fully vested and expected to vest exercisable options that may be converted into shares under option plan. Includes, but is not limited to, unvested options for which requisite service period has not been rendered but that are expected to vest based on achievement of performance condition, if forfeitures are recognized when they occur.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (e)(2)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480429/718-10-50-2

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- Definition

Weighted-average exercise price, at which grantee can acquire shares reserved for issuance, for fully vested and expected to vest exercisable or convertible options. Includes, but is not limited to, unvested options for which requisite service period has not been rendered but that are expected to vest based on achievement of performance condition, if forfeitures are recognized when they occur.

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Number of fully vested and expected to vest options outstanding that can be converted into shares under option plan. Includes, but is not limited to, unvested options for which requisite service period has not been rendered but that are expected to vest based on achievement of performance condition, if forfeitures are recognized when they occur.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (e)(1)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480429/718-10-50-2

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Weighted-average exercise price, at which grantee can acquire shares reserved for issuance, for fully vested and expected to vest options outstanding. Includes, but is not limited to, unvested options for which requisite service period has not been rendered but that are expected to vest based on achievement of performance condition, if forfeitures are recognized when they occur.

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- Definition

Weighted average price at which grantees could have acquired the underlying shares with respect to stock options that were terminated.

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- Definition

Weighted average remaining contractual term for option awards outstanding, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

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-Topic 718
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Weighted average remaining contractual term for fully vested and expected to vest exercisable or convertible options, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days. Includes, but is not limited to, unvested options for which requisite service period has not been rendered but that are expected to vest based on achievement of performance condition, if forfeitures are recognized when they occur.

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Weighted average remaining contractual term for fully vested and expected to vest options outstanding, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days. Includes, but is not limited to, unvested options for which requisite service period has not been rendered but that are expected to vest based on achievement of performance condition, if forfeitures are recognized when they occur.

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