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Fees and Related Party Transactions (Details) - USD ($)
3 Months Ended
Mar. 31, 2020
Mar. 31, 2019
Advisory Fees [Abstract]    
Advisory fees at annual rate of the Members' Capital 1.50%  
Advisory fees $ 101,551 $ 102,095
Sponsor Fees [Abstract]    
Sponsor Fees $ 53,786 54,113
Incentive Allocation [Abstract]    
Percentage of incentive allocation 20.00%  
Incentive Allocation allocated to the Fund by GAIT $ 71,227 0
Administrator's Fee [Abstract]    
Administrator's fees $ 8,599 $ 9,250
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%