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Segments - Schedule of Segment Reporting Information by Segment (Details) - USD ($)
$ in Thousands
 3 Months Ended 9 Months Ended
Sep. 30, 2025
Sep. 30, 2024
Sep. 30, 2025
Sep. 30, 2024
Segment Reporting Information [Line Items]        
Total revenues $ 216,166 $ 195,034 $ 661,730 $ 607,536
Interest expense from finance leases 553 729 1,957 2,208
Gross profit 84,553 93,319 267,092 290,014
Stock based compensation (direct) 3,300 4,000 9,800 12,900
(Gain) loss on disposition of assets (19) 6 (99) (57)
Interest expense, net 20,791 18,369 56,317 54,291
Closure and impairment charges 612 366 7,613 1,442
Amortization of intangible assets 2,905 2,724 8,315 8,169
Loss on extinguishment of debt 0 0 850 0
Income before income taxes 10,064 26,464 41,790 81,734
Advertising revenues        
Segment Reporting Information [Line Items]        
Revenues excluding advertising revenue 68,246 69,789 212,245 219,568
Operating Segments        
Segment Reporting Information [Line Items]        
Total revenues 216,200 195,000 661,700 607,500
Interest expense from finance leases 700 700 2,100 2,200
Depreciation and amortization 3,400 2,600 9,900 8,100
Other segment items 59,300 28,600 170,400 87,600
Gross profit 84,600 93,300 267,100 290,000
Stock based compensation (direct) 800 1,600 2,800 4,800
(Gain) loss on disposition of assets (0) (0) (100) (100)
Other G&A expenses (direct and allocated) 33,100 28,300 99,600 88,300
Segment operating profit (loss) 50,600 63,500 164,700 196,900
Operating Segments | Advertising revenues        
Segment Reporting Information [Line Items]        
Revenues excluding advertising revenue 68,200 69,800 212,200 219,600
Operating Segments | Revenues excluding advertising revenue        
Segment Reporting Information [Line Items]        
Revenues excluding advertising revenue 147,900 125,200 449,500 388,000
Operating Segments | Franchise Segment        
Segment Reporting Information [Line Items]        
Total revenues 161,300 166,400 502,300 518,700
Interest expense from finance leases 0 0 0 0
Depreciation and amortization 100 100 400 300
Other segment items 10,100 9,800 33,400 31,300
Gross profit 82,900 86,600 256,200 267,600
Stock based compensation (direct) 800 1,600 2,800 4,800
(Gain) loss on disposition of assets (0) (0) (100) (100)
Other G&A expenses (direct and allocated) 31,300 28,300 94,500 88,300
Segment operating profit (loss) 50,900 56,800 159,000 174,500
Operating Segments | Franchise Segment | Advertising revenues        
Segment Reporting Information [Line Items]        
Revenues excluding advertising revenue 68,200 69,800 212,200 219,600
Operating Segments | Franchise Segment | Revenues excluding advertising revenue        
Segment Reporting Information [Line Items]        
Revenues excluding advertising revenue 93,100 96,600 290,000 299,200
Operating Segments | Company Restaurants Segment        
Segment Reporting Information [Line Items]        
Total revenues 27,500 300 77,300 800
Interest expense from finance leases 0 0 0 0
Depreciation and amortization 900 0 2,200 100
Other segment items 31,200 300 82,800 800
Gross profit (4,500) 0 (7,600) (100)
Stock based compensation (direct) 0 0 0 0
(Gain) loss on disposition of assets 0 0 0 0
Other G&A expenses (direct and allocated) 1,900 0 5,200 0
Segment operating profit (loss) (6,400) 0 (12,800) (100)
Operating Segments | Company Restaurants Segment | Advertising revenues        
Segment Reporting Information [Line Items]        
Revenues excluding advertising revenue 0 0 0 0
Operating Segments | Company Restaurants Segment | Revenues excluding advertising revenue        
Segment Reporting Information [Line Items]        
Revenues excluding advertising revenue 27,500 300 77,300 800
Operating Segments | Rental        
Segment Reporting Information [Line Items]        
Total revenues 27,000 28,000 81,200 86,500
Interest expense from finance leases 700 700 2,100 2,200
Depreciation and amortization 2,400 2,500 7,300 7,700
Other segment items 18,000 18,400 54,100 55,300
Gross profit 5,900 6,400 17,800 21,300
Stock based compensation (direct) 0 0 0 0
(Gain) loss on disposition of assets 0 0 0 0
Other G&A expenses (direct and allocated) 0 0 0 0
Segment operating profit (loss) 5,900 6,400 17,800 21,300
Operating Segments | Rental | Advertising revenues        
Segment Reporting Information [Line Items]        
Revenues excluding advertising revenue 0 0 0 0
Operating Segments | Rental | Revenues excluding advertising revenue        
Segment Reporting Information [Line Items]        
Revenues excluding advertising revenue 27,000 28,000 81,200 86,500
Operating Segments | Financing        
Segment Reporting Information [Line Items]        
Total revenues 300 400 900 1,400
Interest expense from finance leases 0 0 0 0
Depreciation and amortization 0 0 0 0
Other segment items 100 100 200 200
Gross profit 200 300 800 1,200
Stock based compensation (direct) 0 0 0 0
(Gain) loss on disposition of assets 0 0 0 0
Other G&A expenses (direct and allocated) 0 0 0 0
Segment operating profit (loss) 200 300 800 1,200
Operating Segments | Financing | Advertising revenues        
Segment Reporting Information [Line Items]        
Revenues excluding advertising revenue 0 0 0 0
Operating Segments | Financing | Revenues excluding advertising revenue        
Segment Reporting Information [Line Items]        
Revenues excluding advertising revenue 300 400 900 1,400
Segment Reporting Excluding Corporate Expenditure        
Segment Reporting Information [Line Items]        
Depreciation and amortization 4,200 4,300 13,100 12,800
Stock based compensation (direct) 2,300 2,300 6,900 7,800
Other G&A expenses (direct and allocated) 9,700 9,000 29,800 30,700
Interest expense, net 20,800 18,400 56,300 54,300
Closure and impairment charges 600 400 7,600 1,400
Amortization of intangible assets 2,900 2,700 8,300 8,200
Loss on extinguishment of debt 0 0 900 0
Income before income taxes $ 10,100 $ 26,500 $ 41,800 $ 81,700