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Fees and Related Party Transactions (Details) - USD ($)
12 Months Ended
Dec. 31, 2019
Dec. 31, 2018
Advisory Fees [Abstract]    
Advisory fees $ 424,019 $ 523,762
Advisory fees at annual rate of the Members' Capital 1.50%  
Sponsor Fees [Abstract]    
Sponsor Fees $ 224,152 $ 272,976
Incentive Allocation [Abstract]    
Percentage of incentive allocation 20.00% 20.00%
Incentive Allocation allocated to the Fund by GAIT $ 0 $ 0
Administrator's Fee [Abstract]    
Administrator's fees $ 36,865 $ 45,411
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%