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Fees and Related Party Transactions (Details) - USD ($)
3 Months Ended 9 Months Ended
Sep. 30, 2019
Sep. 30, 2018
Sep. 30, 2019
Sep. 30, 2018
Advisory Fees [Abstract]        
Advisory fees at annual rate of the Members' Capital     1.50%  
Advisory fees $ 111,466 $ 131,072 $ 317,862 $ 409,370
Sponsor Fees [Abstract]        
Sponsor Fees 58,599 67,645 $ 167,668 212,548
Incentive Allocation [Abstract]        
Percentage of incentive allocation     20.00%  
Incentive Allocation allocated to the Fund by GAIT     $ 0 0
Administrator's Fee [Abstract]        
Administrator's fees $ 9,503 $ 11,420 $ 27,879 $ 35,389
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%