| Pay vs Performance Disclosure - USD ($) | 3 Months Ended | 12 Months Ended | 19 Months Ended |
| Dec. 31, 2021 | Feb. 24, 2023 | Feb. 25, 2022 | Feb. 26, 2021 | Sep. 30, 2021 |
| Pay vs Performance Disclosure [Table] | | | | | |
| Pay vs Performance [Table Text Block] | | Summary Compensation Table Total for PEO 1 Compensation Actually Paid to PEO 2 Value of Initial Fixed $100 Investment Based On: Fiscal Year Sara E. Armbruster James P. Keane Sara E. Armbruster James P. Keane Average Summary Compensation Table Total for Non-PEO Named Executive Officers 1 Average Compensation Actually Paid to Non-PEO Named Executive Officers 2 Total Shareholder Return 3 Peer Group Total Shareholder Return 3 Net Income ($ in millions) Operating Income, as adjusted ($ in millions) 4 (a) (b) (b) (c) (c) (d) (e) (f) (g) (h) (i) 2023 $ 4,150,404 $ — $ 1,987,633 $ — $ 1,737,242 $ 1,205,950 $ 57 $ 81 $ 35.3 $ 89.9 2022 $ 5,420,546 $ 6,324,983 $ 4,795,416 $ 2,788,222 $ 1,212,915 $ 822,301 $ 82 $ 113 $ 4.0 $ 19.3 2021 $ — $ 7,407,174 $ — $ 6,841,476 $ 1,574,431 $ 1,445,052 $ 88 $ 107 $ 26.1 $ 89.2 | | | |
| Company Selected Measure Name | | operating income | | | |
| Named Executive Officers, Footnote [Text Block] | | The amounts reported in columns (b) reflect total compensation reported in the Summary Compensation Table for Sara Armbruster and James Keane for the fiscal years in which they served as our PEO. For the fiscal years reported in the table, James Keane was our PEO from the beginning of fiscal year 2021 to October 2021, and Sara Armbruster was our PEO from October 2021 to the end of fiscal year 2023. The amounts reported in column (d) reflect the average total compensation reported in the Summary Compensation Table for the Non-PEO Named Executive Officers for the applicable fiscal years as listed below: 2023 2022 2021 David C. Sylvester David C. Sylvester David C. Sylvester Allan W. Smith, Jr. Allan W. Smith, Jr. Lizbeth S. O’Shaughnessy Lizbeth S. O’Shaughnessy Lizbeth S. O’Shaughnessy Sara E. Armbruster Robert G. Krestakos Robert G. Krestakos Allan W. Smith, Jr. James N. Ludwig Eddy F. Schmitt | | | |
| Peer Group Issuers, Footnote [Text Block] | | The dollar amounts in columns (f) and (g) represent TSR, calculated as the value at the end of the applicable fiscal year of an assumed $100 investment in our Class A Common Stock and a peer group, respectively, on the last trading day of fiscal year 2021. The peer group consists of Kimball International, Inc., HNI Corporation and MillerKnoll, Inc. (prior to their merger on July 19, 2021, the peer group included both Herman Miller, Inc. and Knoll, Inc.). The returns of each company in the peer group are weighted by their relative market capitalization at the beginning of each fiscal year. | | | |
| Adjustment To PEO Compensation, Footnote [Text Block] | | The following table reconciles Compensation Actually Paid to the Summary Compensation Table Total for Sara Armbruster and James Keane. 2023 2022 2021 PEOs Sara E. Armbruster Sara E. Armbruster James P. Keane James P. Keane Summary Compensation Table Total (column b) $ 4,150,404 $ 5,420,546 $ 6,324,983 $ 7,407,174 – Reported value of equity-based awards $ (2,347,280) $ (4,462,068) $ (5,057,410) $ (4,808,704) + Fiscal year-end fair value of outstanding and unvested equity-based awards granted in applicable fiscal year $ 1,382,154 $ 3,723,104 $ 2,139,814 $ 4,434,838 + Change in fair value of outstanding and unvested equity-based awards granted in prior fiscal years $ (1,132,864) $ (53,677) $ (516,320) $ (413,500) + Fair value as of vesting date of equity-based awards granted and vested in the applicable fiscal year $ 47,312 $ 12,786 $ 111,510 $ 1,336,846 + Change in fair value of equity-based awards granted in prior fiscal years that vested in the applicable fiscal year $ (413,320) $ (66,910) $ (583,160) $ (1,352,650) + Value of dividends or other earnings paid on equity-based awards not otherwise reflected in total compensation $ 208,857 $ 118,563 $ 368,805 $ 255,437 – Aggregate change in the actuarial present value of accumulated benefits under defined benefit and actuarial pension plans $ — $ — $ — $ (17,965) + Service cost of actuarial present value of benefits under defined benefit and actuarial pension plans $ 92,370 $ 103,072 $ — $ — Total adjustments $ (2,162,771) $ (625,130) $ (3,536,761) $ (565,698) Equals: Compensation Actually Paid (column c) $ 1,987,633 $ 4,795,416 $ 2,788,222 $ 6,841,476 | | | |
| Non-PEO NEO Average Total Compensation Amount | | $ 1,737,242 | $ 1,212,915 | $ 1,574,431 | |
| Non-PEO NEO Average Compensation Actually Paid Amount | | $ 1,205,950 | 822,301 | 1,445,052 | |
| Adjustment to Non-PEO NEO Compensation Footnote [Text Block] | | The following table reconciles Compensation Actually Paid to the Summary Compensation Table Total for the average of the Non-PEO Named Executive Officers: Average for Non-PEO Named Executive Officers 2023 2022 2021 Summary Compensation Table Total (column d) $ 1,737,242 $ 1,212,915 $ 1,574,431 – Reported value of equity-based awards $ (825,775) $ (611,901) $ (760,192) + Fiscal year-end fair value of outstanding and unvested equity-based awards granted in applicable fiscal year $ 450,729 $ 278,335 $ 641,759 + Change in fair value of outstanding and unvested equity-based awards granted in prior fiscal years $ (108,729) $ (60,239) $ (66,718) + Fair value as of vesting date of equity-based awards granted and vested in the applicable fiscal year $ 61,160 $ 14,050 $ 250,223 + Change in fair value of equity-based awards granted in prior fiscal years that vested in the applicable fiscal year $ (173,205) $ (75,576) $ (222,513) + Value of dividends or other earnings paid on equity-based awards not otherwise reflected in total compensation $ 64,528 $ 46,577 $ 42,306 – Aggregate change in the actuarial prevent value of accumulated benefits under defined benefit and actuarial pension plans $ — $ — $ (38,770) + Service cost of actuarial present value of benefits under defined benefit and actuarial pension plans $ — $ 18,140 $ 24,526 Total adjustments $ (531,292) $ (390,614) $ (129,379) Equals: Compensation Actually Paid (column e) $ 1,205,950 $ 822,301 $ 1,445,052 | | | |
| Compensation Actually Paid vs. Total Shareholder Return [Text Block] | | | | | |
| Compensation Actually Paid vs. Net Income [Text Block] | | | | | |
| Compensation Actually Paid vs. Company Selected Measure [Text Block] | | | | | |
| Total Shareholder Return Vs Peer Group [Text Block] | | | | | |
| Tabular List [Table Text Block] | | Tabular List of Financial Performance Measures Net Income * Operating Income * Revenue * Relative Total Shareholder Return Return on Invested Capital * | | | |
| Total Shareholder Return Amount | | $ 57 | 82 | 88 | |
| Peer Group Total Shareholder Return Amount | | 81 | 113 | 107 | |
| Net Income (Loss) | | $ 35,300,000 | $ 4,000,000 | $ 26,100,000 | |
| Company Selected Measure Amount | | 89,900,000 | 19,300,000 | 89,200,000 | |
| Additional 402(v) Disclosure [Text Block] | | The amounts reported in columns (c) and (e) represent Compensation Actually Paid to each of the PEOs and the average Compensation Actually Paid to the Non-PEO Named Executive Officers, respectively, calculated in accordance with Item 402(v) of Regulation S-K. Total compensation reported in the Summary Compensation Table is the starting point to determine Compensation Actually Paid, and then certain adjustments are made to those amounts with respect to equity-based and other compensation, as detailed below.For equity-based awards granted during the fiscal year, the amount reported in the Stock Awards column of the Summary Compensation Table is replaced with the fair value of the awards at the end of the fiscal year or on the vesting date, if earlier. For equity-based awards made in prior fiscal years which vested during the fiscal year, the change in fair value from the end of the prior fiscal year to the vesting date is added, and for equity-based awards made in prior fiscal years that remained unvested at fiscal year end, the change in fair value from the end of the prior fiscal year to the end of the fiscal year is added. For any equity-based awards granted in a prior fiscal year that failed to meet the applicable vesting requirements during the fiscal year, the fair value at the end of the prior year is deducted. Finally, the dollar value of any dividends or other earnings paid on any equity-based awards in the fiscal year prior to the vesting date that are not otherwise included in total compensation are added. For defined benefit and actuarial pension plans, the aggregate change in the actuarial present value of the NEO’s accumulated benefits under all such plans is replaced with the (i) service cost, calculated as the actuarial present value of the NEO’s benefits under all such plans attributable to services rendered during the fiscal year, and (ii) prior service cost, calculated as the entire cost of benefits granted (or credit for benefits reduced) in a plan amendment (or initiation) during the fiscal year that are attributed by the benefit formula to services rendered in periods prior to the amendment. | | | |
| Measure [Axis]: 1 | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Measure Name | | Net Income * | | | |
| Measure [Axis]: 2 | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Measure Name | | Operating Income * | | | |
| Measure [Axis]: 3 | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Measure Name | | Revenue * | | | |
| Measure [Axis]: 4 | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Measure Name | | Relative Total Shareholder Return | | | |
| Measure [Axis]: 5 | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Measure Name | | Return on Invested Capital * | | | |
| Sara E. Armbruster [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| PEO Total Compensation Amount | | $ 4,150,404 | $ 5,420,546 | | |
| PEO Actually Paid Compensation Amount | | $ 1,987,633 | $ 4,795,416 | | |
| PEO Name | Sara Armbruste | Sara Armbruste | Sara Armbruste | | |
| James P. Keane [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| PEO Total Compensation Amount | | | $ 6,324,983 | $ 7,407,174 | |
| PEO Actually Paid Compensation Amount | | | 2,788,222 | 6,841,476 | |
| PEO Name | | | | | James Keane |
| PEO [Member] | Sara E. Armbruster [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | $ (2,162,771) | (625,130) | | |
| PEO [Member] | Sara E. Armbruster [Member] | Equity Awards Reported Value [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | (2,347,280) | (4,462,068) | | |
| PEO [Member] | Sara E. Armbruster [Member] | Awards Granted During the Year, Unvested [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | 1,382,154 | 3,723,104 | | |
| PEO [Member] | Sara E. Armbruster [Member] | Equity Awards Granted in Prior Years, Unvested [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | (1,132,864) | (53,677) | | |
| PEO [Member] | Sara E. Armbruster [Member] | Awards Granted During the Year, Vested [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | 47,312 | 12,786 | | |
| PEO [Member] | Sara E. Armbruster [Member] | Equity Awards Granted in Prior Years, Vested [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | (413,320) | (66,910) | | |
| PEO [Member] | Sara E. Armbruster [Member] | Equity Awards, Value of Dividends and Other Earnings Paid Adjustment [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | 208,857 | 118,563 | | |
| PEO [Member] | Sara E. Armbruster [Member] | Change in Pension Value [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | 0 | 0 | | |
| PEO [Member] | Sara E. Armbruster [Member] | Pension Adjustments, Service Cost [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | 92,370 | 103,072 | | |
| PEO [Member] | James P. Keane [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | | (3,536,761) | (565,698) | |
| PEO [Member] | James P. Keane [Member] | Equity Awards Reported Value [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | | (5,057,410) | (4,808,704) | |
| PEO [Member] | James P. Keane [Member] | Awards Granted During the Year, Unvested [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | | 2,139,814 | 4,434,838 | |
| PEO [Member] | James P. Keane [Member] | Equity Awards Granted in Prior Years, Unvested [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | | (516,320) | (413,500) | |
| PEO [Member] | James P. Keane [Member] | Awards Granted During the Year, Vested [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | | 111,510 | 1,336,846 | |
| PEO [Member] | James P. Keane [Member] | Equity Awards Granted in Prior Years, Vested [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | | (583,160) | (1,352,650) | |
| PEO [Member] | James P. Keane [Member] | Equity Awards, Value of Dividends and Other Earnings Paid Adjustment [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | | 368,805 | 255,437 | |
| PEO [Member] | James P. Keane [Member] | Change in Pension Value [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | | 0 | (17,965) | |
| PEO [Member] | James P. Keane [Member] | Pension Adjustments, Service Cost [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | | 0 | 0 | |
| Non-PEO NEO [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | (531,292) | (390,614) | (129,379) | |
| Non-PEO NEO [Member] | Equity Awards Reported Value [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | (825,775) | (611,901) | (760,192) | |
| Non-PEO NEO [Member] | Awards Granted During the Year, Unvested [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | 450,729 | 278,335 | 641,759 | |
| Non-PEO NEO [Member] | Equity Awards Granted in Prior Years, Unvested [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | (108,729) | (60,239) | (66,718) | |
| Non-PEO NEO [Member] | Awards Granted During the Year, Vested [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | 61,160 | 14,050 | 250,223 | |
| Non-PEO NEO [Member] | Equity Awards Granted in Prior Years, Vested [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | (173,205) | (75,576) | (222,513) | |
| Non-PEO NEO [Member] | Equity Awards, Value of Dividends and Other Earnings Paid Adjustment [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | 64,528 | 46,577 | 42,306 | |
| Non-PEO NEO [Member] | Change in Pension Value [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | 0 | 0 | (38,770) | |
| Non-PEO NEO [Member] | Pension Adjustments, Service Cost [Member] | | | | | |
| Pay vs Performance Disclosure [Table] | | | | | |
| Adjustment to Compensation Amount | | $ 0 | $ 18,140 | $ 24,526 | |
