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Segment Reporting (Details) - USD ($)
$ in Thousands
 12 Months Ended
Dec. 31, 2024
Dec. 31, 2023
Dec. 31, 2022
Segment Reporting Information [Line Items]      
Total revenues $ 812,306 $ 831,068 $ 909,402
Interest expense from finance leases 2,904 2,771 2,962
Gross profit 375,309 396,684 377,358
Stock based compensation (direct) 16,300 10,600 17,600
(Gain) loss on disposition of assets (3,150) 2,350 (2,536)
Interest expense, net 72,142 70,047 60,952
Closure and impairment charges 9,240 3,594 3,062
Amortization of intangible assets 10,832 10,923 10,559
Loss (gain) on extinguishment of debt 0 10 (210)
Income before income taxes 89,543 111,703 114,785
Advertising revenues      
Segment Reporting Information [Line Items]      
Revenues excluding advertising revenue 290,436 300,796 289,328
Operating Segments      
Segment Reporting Information [Line Items]      
Total revenues 812,300 831,100 909,400
Interest expense from finance leases 2,900 2,800 3,000
Depreciation and amortization 11,000 11,400 15,500
Other segment items 132,700 119,400 224,300
Gross profit 375,300 396,700 377,300
Stock based compensation (direct) 5,700 2,500 6,000
(Gain) loss on disposition of assets (3,200) 600 (2,500)
Other G&A expenses (direct and allocated) 119,300 126,900 113,500
Segment operating profit 253,500 266,700 260,300
Operating Segments | Advertising revenues      
Segment Reporting Information [Line Items]      
Revenues excluding advertising revenue 290,400 300,800 289,300
Operating Segments | Revenues excluding advertising revenue      
Segment Reporting Information [Line Items]      
Revenues excluding advertising revenue 521,900 530,300 620,100
Operating Segments | Franchise      
Segment Reporting Information [Line Items]      
Total revenues 686,000 706,400 662,400
Interest expense from finance leases 0 0 0
Depreciation and amortization 1,400 1,100 4,800
Other segment items 48,000 42,500 27,900
Gross profit 346,100 362,000 340,500
Stock based compensation (direct) 5,700 2,500 6,000
(Gain) loss on disposition of assets 0 0 0
Other G&A expenses (direct and allocated) 119,300 126,900 113,500
Segment operating profit 221,000 232,500 221,000
Operating Segments | Franchise | Advertising revenues      
Segment Reporting Information [Line Items]      
Revenues excluding advertising revenue 290,400 300,800 289,300
Operating Segments | Franchise | Revenues excluding advertising revenue      
Segment Reporting Information [Line Items]      
Revenues excluding advertising revenue 395,500 405,600 373,100
Operating Segments | Company Restaurants      
Segment Reporting Information [Line Items]      
Total revenues 9,300 2,100 126,900
Interest expense from finance leases 0 0 0
Depreciation and amortization (600) (200) 0
Other segment items 10,500 2,400 121,700
Gross profit (600) 0 5,200
Stock based compensation (direct) 0 0 0
(Gain) loss on disposition of assets (2,200) 200 (0)
Other G&A expenses (direct and allocated) 0 0 0
Segment operating profit 1,600 (200) 5,200
Operating Segments | Company Restaurants | Advertising revenues      
Segment Reporting Information [Line Items]      
Revenues excluding advertising revenue 0 0 0
Operating Segments | Company Restaurants | Revenues excluding advertising revenue      
Segment Reporting Information [Line Items]      
Revenues excluding advertising revenue 9,300 2,100 126,900
Operating Segments | Rental      
Segment Reporting Information [Line Items]      
Total revenues 115,300 120,000 116,500
Interest expense from finance leases 2,900 2,800 3,000
Depreciation and amortization 10,100 10,500 10,700
Other segment items 73,900 74,200 74,300
Gross profit 28,400 32,500 28,500
Stock based compensation (direct) 0 0 0
(Gain) loss on disposition of assets (1,000) 300 (2,500)
Other G&A expenses (direct and allocated) 0 0 0
Segment operating profit 29,400 32,200 31,000
Operating Segments | Rental | Advertising revenues      
Segment Reporting Information [Line Items]      
Revenues excluding advertising revenue 0 0 0
Operating Segments | Rental | Revenues excluding advertising revenue      
Segment Reporting Information [Line Items]      
Revenues excluding advertising revenue 115,300 120,000 116,500
Operating Segments | Financing      
Segment Reporting Information [Line Items]      
Total revenues 1,800 2,600 3,600
Interest expense from finance leases 0 0 0
Depreciation and amortization 0 0 0
Other segment items 300 400 400
Gross profit 1,500 2,200 3,200
Stock based compensation (direct) 0 0 0
(Gain) loss on disposition of assets 0 0 0
Other G&A expenses (direct and allocated) 0 0 0
Segment operating profit 1,500 2,200 3,200
Operating Segments | Financing | Advertising revenues      
Segment Reporting Information [Line Items]      
Revenues excluding advertising revenue 0 0 0
Operating Segments | Financing | Revenues excluding advertising revenue      
Segment Reporting Information [Line Items]      
Revenues excluding advertising revenue 1,800 2,600 3,600
Segment Reporting Excluding Corporate Expenditure      
Segment Reporting Information [Line Items]      
Depreciation and amortization 17,400 13,300 11,900
Stock based compensation (direct) 10,200 9,500 10,100
(Gain) loss on disposition of assets   1,800  
Other G&A expenses (direct and allocated) 44,200 45,800 49,100
Interest expense, net 72,100 70,100 60,900
Closure and impairment charges 9,300 3,600 3,100
Amortization of intangible assets 10,800 10,900 10,600
Loss (gain) on extinguishment of debt     (200)
Income before income taxes $ 89,500 $ 111,700 $ 114,800