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Fees and Related Party Transactions (Details) - USD ($)
3 Months Ended 6 Months Ended
Jun. 30, 2020
Jun. 30, 2019
Jun. 30, 2020
Jun. 30, 2019
Advisory Fees [Abstract]        
Advisory fees at annual rate of the Members' Capital     1.50%  
Advisory fees $ 102,681 $ 104,301 $ 204,232 $ 206,396
Sponsor Fees [Abstract]        
Sponsor Fees 54,080 54,956 $ 107,866 109,069
Incentive Allocation [Abstract]        
Percentage of incentive allocation     20.00%  
Incentive Allocation allocated to the Fund by GAIT 5,975 0 $ 77,202 0
Administrator's Fee [Abstract]        
Administrator's fees $ 9,018 $ 9,126 $ 17,617 $ 18,376
Class 0 Units [Member]        
Sponsor Fees [Abstract]        
Sponsor fees at annual rate of the Members' Capital     0.50%  
Class 2 Units [Member]        
Sponsor Fees [Abstract]        
Sponsor fees at annual rate of the Members' Capital     1.25%