Setup item 1: ( { g s k } k ∈ [ d ] , { g l l i ( s ) , g r r i ( s ) , g o o i ( s ) } i ∈ { 0 , . . . , n } , { g l α l l i ( s ) , g r α r r i ( s ) , g o α o o i ( s ) , g l β l i ( s ) g r β r i ( s ) g o β o i ( s ) } i ∈ { m + 1 , . . . , n } , g l t ( s ) , g r t ( s ) , g o t ( s ) , g l α l t ( s ) , g r α r t ( s ) , g o α o t ( s ) , g l β t ( s ) , g r β t ( s ) , g o β t ( s ) ) 2. item 2