Commitments and Contingencies (Narrative) (Details)	3 Months Ended
Dec. 31, 2024 USD ($)
2005 Incentive Compensation Plan \| Amended 2011 Principal Shareholder Employment Agreement
Income tax obligation relating to the payout of the life insurance policy	$ 500,000

The amount of cash outflow for the payment of income tax expense pertaining to pay out of life insurance policy.

No definition available.

Name:	sga_PaymentOfIncomeTaxExpensePayoutOfLifeInsurancePolicy
Namespace Prefix:	sga_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration