Omar $($single$)$ is a $50$ percent owner in Cougar LLC $($taxed as a partnership$).$ Omar works half time for Cougar and receives guaranteed payment of $$50,000.$ Cougar LLC reported $$450,000$ of business income for the year $(2023).$ Before considering his $50$ percent business income allocation from Cougar and the self$-$employment tax deduction $($if any$),$ Omar's adjusted gross income is $$210,000($includes $$50,000$ guaranteed payment from Cougar and $$180,000$ salary from a different employer$).$ Omar reports itemized deductions of $$40,000.$ Answer the following questions for Omar.

b$.$ What would be Omar's self$-$employment tax liability if he didn't receive any salary?