Function isValidScrollDirectionList

Returns directions is
    | "none"
    | "left"
    | "right"
    | "up"
    | "down"
    | "ambiguous"
    | "up,down"
    | "down,up"
    | "right,up"
    | "right,down"
    | "right,up,down"
    | "right,down,up"
    | "down,right"
    | "up,right"
    | "up,right,down"
    | "up,down,right"
    | "down,right,up"
    | "down,up,right"
    | "left,right"
    | "left,up"
    | "left,down"
    | "left,up,down"
    | "left,down,up"
    | "left,right,up"
    | "left,right,down"
    | "left,right,up,down"
    | "left,right,down,up"
    | "left,down,right"
    | "left,up,right"
    | "left,up,right,down"
    | "left,up,down,right"
    | "left,down,right,up"
    | "left,down,up,right"
    | "down,left"
    | "up,left"
    | "up,left,down"
    | "up,down,left"
    | "down,left,up"
    | "down,up,left"
    | "right,left"
    | "right,left,up"
    | "right,left,down"
    | "right,left,up,down"
    | "right,left,down,up"
    | "right,down,left"
    | "right,up,left"
    | "right,up,left,down"
    | "right,up,down,left"
    | "right,down,left,up"
    | "right,down,up,left"
    | "down,left,right"
    | "down,right,left"
    | "up,left,right"
    | "up,left,right,down"
    | "up,left,down,right"
    | "up,right,left"
    | "up,right,left,down"
    | "up,right,down,left"
    | "up,down,left,right"
    | "up,down,right,left"
    | "down,left,right,up"
    | "down,left,up,right"
    | "down,right,left,up"
    | "down,right,up,left"
    | "down,up,left,right"
    | "down,up,right,left"
    | "ambiguous,left"
    | "ambiguous,right"
    | "ambiguous,up"
    | "ambiguous,down"
    | "ambiguous,up,down"
    | "ambiguous,down,up"
    | "ambiguous,right,up"
    | "ambiguous,right,down"
    | "ambiguous,right,up,down"
    | "ambiguous,right,down,up"
    | "ambiguous,down,right"
    | "ambiguous,up,right"
    | "ambiguous,up,right,down"
    | "ambiguous,up,down,right"
    | "ambiguous,down,right,up"
    | "ambiguous,down,up,right"
    | "ambiguous,left,right"
    | "ambiguous,left,up"
    | "ambiguous,left,down"
    | "ambiguous,left,up,down"
    | "ambiguous,left,down,up"
    | "ambiguous,left,right,up"
    | "ambiguous,left,right,down"
    | "ambiguous,left,right,up,down"
    | "ambiguous,left,right,down,up"
    | "ambiguous,left,down,right"
    | "ambiguous,left,up,right"
    | "ambiguous,left,up,right,down"
    | "ambiguous,left,up,down,right"
    | "ambiguous,left,down,right,up"
    | "ambiguous,left,down,up,right"
    | "ambiguous,down,left"
    | "ambiguous,up,left"
    | "ambiguous,up,left,down"
    | "ambiguous,up,down,left"
    | "ambiguous,down,left,up"
    | "ambiguous,down,up,left"
    | "ambiguous,right,left"
    | "ambiguous,right,left,up"
    | "ambiguous,right,left,down"
    | "ambiguous,right,left,up,down"
    | "ambiguous,right,left,down,up"
    | "ambiguous,right,down,left"
    | "ambiguous,right,up,left"
    | "ambiguous,right,up,left,down"
    | "ambiguous,right,up,down,left"
    | "ambiguous,right,down,left,up"
    | "ambiguous,right,down,up,left"
    | "ambiguous,down,left,right"
    | "ambiguous,down,right,left"
    | "ambiguous,up,left,right"
    | "ambiguous,up,left,right,down"
    | "ambiguous,up,left,down,right"
    | "ambiguous,up,right,left"
    | "ambiguous,up,right,left,down"
    | "ambiguous,up,right,down,left"
    | "ambiguous,up,down,left,right"
    | "ambiguous,up,down,right,left"
    | "ambiguous,down,left,right,up"
    | "ambiguous,down,left,up,right"
    | "ambiguous,down,right,left,up"
    | "ambiguous,down,right,up,left"
    | "ambiguous,down,up,left,right"
    | "ambiguous,down,up,right,left"
    | "down,ambiguous"
    | "up,ambiguous"
    | "up,ambiguous,down"
    | "up,down,ambiguous"
    | "down,ambiguous,up"
    | "down,up,ambiguous"
    | "right,ambiguous"
    | "right,ambiguous,up"
    | "right,ambiguous,down"
    | "right,ambiguous,up,down"
    | "right,ambiguous,down,up"
    | "right,down,ambiguous"
    | "right,up,ambiguous"
    | "right,up,ambiguous,down"
    | "right,up,down,ambiguous"
    | "right,down,ambiguous,up"
    | "right,down,up,ambiguous"
    | "down,ambiguous,right"
    | "down,right,ambiguous"
    | "up,ambiguous,right"
    | "up,ambiguous,right,down"
    | "up,ambiguous,down,right"
    | "up,right,ambiguous"
    | "up,right,ambiguous,down"
    | "up,right,down,ambiguous"
    | "up,down,ambiguous,right"
    | "up,down,right,ambiguous"
    | "down,ambiguous,right,up"
    | "down,ambiguous,up,right"
    | "down,right,ambiguous,up"
    | "down,right,up,ambiguous"
    | "down,up,ambiguous,right"
    | "down,up,right,ambiguous"
    | "left,ambiguous"
    | "left,ambiguous,right"
    | "left,ambiguous,up"
    | "left,ambiguous,down"
    | "left,ambiguous,up,down"
    | "left,ambiguous,down,up"
    | "left,ambiguous,right,up"
    | "left,ambiguous,right,down"
    | "left,ambiguous,right,up,down"
    | "left,ambiguous,right,down,up"
    | "left,ambiguous,down,right"
    | "left,ambiguous,up,right"
    | "left,ambiguous,up,right,down"
    | "left,ambiguous,up,down,right"
    | "left,ambiguous,down,right,up"
    | "left,ambiguous,down,up,right"
    | "left,down,ambiguous"
    | "left,up,ambiguous"
    | "left,up,ambiguous,down"
    | "left,up,down,ambiguous"
    | "left,down,ambiguous,up"
    | "left,down,up,ambiguous"
    | "left,right,ambiguous"
    | "left,right,ambiguous,up"
    | "left,right,ambiguous,down"
    | "left,right,ambiguous,up,down"
    | "left,right,ambiguous,down,up"
    | "left,right,down,ambiguous"
    | "left,right,up,ambiguous"
    | "left,right,up,ambiguous,down"
    | "left,right,up,down,ambiguous"
    | "left,right,down,ambiguous,up"
    | "left,right,down,up,ambiguous"
    | "left,down,ambiguous,right"
    | "left,down,right,ambiguous"
    | "left,up,ambiguous,right"
    | "left,up,ambiguous,right,down"
    | "left,up,ambiguous,down,right"
    | "left,up,right,ambiguous"
    | "left,up,right,ambiguous,down"
    | "left,up,right,down,ambiguous"
    | "left,up,down,ambiguous,right"
    | "left,up,down,right,ambiguous"
    | "left,down,ambiguous,right,up"
    | "left,down,ambiguous,up,right"
    | "left,down,right,ambiguous,up"
    | "left,down,right,up,ambiguous"
    | "left,down,up,ambiguous,right"
    | "left,down,up,right,ambiguous"
    | "down,ambiguous,left"
    | "down,left,ambiguous"
    | "up,ambiguous,left"
    | "up,ambiguous,left,down"
    | "up,ambiguous,down,left"
    | "up,left,ambiguous"
    | "up,left,ambiguous,down"
    | "up,left,down,ambiguous"
    | "up,down,ambiguous,left"
    | "up,down,left,ambiguous"
    | "down,ambiguous,left,up"
    | "down,ambiguous,up,left"
    | "down,left,ambiguous,up"
    | "down,left,up,ambiguous"
    | "down,up,ambiguous,left"
    | "down,up,left,ambiguous"
    | "right,ambiguous,left"
    | "right,ambiguous,left,up"
    | "right,ambiguous,left,down"
    | "right,ambiguous,left,up,down"
    | "right,ambiguous,left,down,up"
    | "right,ambiguous,down,left"
    | "right,ambiguous,up,left"
    | "right,ambiguous,up,left,down"
    | "right,ambiguous,up,down,left"
    | "right,ambiguous,down,left,up"
    | "right,ambiguous,down,up,left"
    | "right,left,ambiguous"
    | "right,left,ambiguous,up"
    | "right,left,ambiguous,down"
    | "right,left,ambiguous,up,down"
    | "right,left,ambiguous,down,up"
    | "right,left,down,ambiguous"
    | "right,left,up,ambiguous"
    | "right,left,up,ambiguous,down"
    | "right,left,up,down,ambiguous"
    | "right,left,down,ambiguous,up"
    | "right,left,down,up,ambiguous"
    | "right,down,ambiguous,left"
    | "right,down,left,ambiguous"
    | "right,up,ambiguous,left"
    | "right,up,ambiguous,left,down"
    | "right,up,ambiguous,down,left"
    | "right,up,left,ambiguous"
    | "right,up,left,ambiguous,down"
    | "right,up,left,down,ambiguous"
    | "right,up,down,ambiguous,left"
    | "right,up,down,left,ambiguous"
    | "right,down,ambiguous,left,up"
    | "right,down,ambiguous,up,left"
    | "right,down,left,ambiguous,up"
    | "right,down,left,up,ambiguous"
    | "right,down,up,ambiguous,left"
    | "right,down,up,left,ambiguous"
    | "down,ambiguous,left,right"
    | "down,ambiguous,right,left"
    | "down,left,ambiguous,right"
    | "down,left,right,ambiguous"
    | "down,right,ambiguous,left"
    | "down,right,left,ambiguous"
    | "up,ambiguous,left,right"
    | "up,ambiguous,left,right,down"
    | "up,ambiguous,left,down,right"
    | "up,ambiguous,right,left"
    | "up,ambiguous,right,left,down"
    | "up,ambiguous,right,down,left"
    | "up,ambiguous,down,left,right"
    | "up,ambiguous,down,right,left"
    | "up,left,ambiguous,right"
    | "up,left,ambiguous,right,down"
    | "up,left,ambiguous,down,right"
    | "up,left,right,ambiguous"
    | "up,left,right,ambiguous,down"
    | "up,left,right,down,ambiguous"
    | "up,left,down,ambiguous,right"
    | "up,left,down,right,ambiguous"
    | "up,right,ambiguous,left"
    | "up,right,ambiguous,left,down"
    | "up,right,ambiguous,down,left"
    | "up,right,left,ambiguous"
    | "up,right,left,ambiguous,down"
    | "up,right,left,down,ambiguous"
    | "up,right,down,ambiguous,left"
    | "up,right,down,left,ambiguous"
    | "up,down,ambiguous,left,right"
    | "up,down,ambiguous,right,left"
    | "up,down,left,ambiguous,right"
    | "up,down,left,right,ambiguous"
    | "up,down,right,ambiguous,left"
    | "up,down,right,left,ambiguous"
    | "down,ambiguous,left,right,up"
    | "down,ambiguous,left,up,right"
    | "down,ambiguous,right,left,up"
    | "down,ambiguous,right,up,left"
    | "down,ambiguous,up,left,right"
    | "down,ambiguous,up,right,left"
    | "down,left,ambiguous,right,up"
    | "down,left,ambiguous,up,right"
    | "down,left,right,ambiguous,up"
    | "down,left,right,up,ambiguous"
    | "down,left,up,ambiguous,right"
    | "down,left,up,right,ambiguous"
    | "down,right,ambiguous,left,up"
    | "down,right,ambiguous,up,left"
    | "down,right,left,ambiguous,up"
    | "down,right,left,up,ambiguous"
    | "down,right,up,ambiguous,left"
    | "down,right,up,left,ambiguous"
    | "down,up,ambiguous,left,right"
    | "down,up,ambiguous,right,left"
    | "down,up,left,ambiguous,right"
    | "down,up,left,right,ambiguous"
    | "down,up,right,ambiguous,left"
    | "down,up,right,left,ambiguous"
    | "none,left"
    | "none,right"
    | "none,up"
    | "none,down"
    | "none,ambiguous"
    | "none,up,down"
    | "none,down,up"
    | "none,right,up"
    | "none,right,down"
    | "none,right,up,down"
    | "none,right,down,up"
    | "none,down,right"
    | "none,up,right"
    | "none,up,right,down"
    | "none,up,down,right"
    | "none,down,right,up"
    | "none,down,up,right"
    | "none,left,right"
    | "none,left,up"
    | "none,left,down"
    | "none,left,up,down"
    | "none,left,down,up"
    | "none,left,right,up"
    | "none,left,right,down"
    | "none,left,right,up,down"
    | "none,left,right,down,up"
    | "none,left,down,right"
    | "none,left,up,right"
    | "none,left,up,right,down"
    | "none,left,up,down,right"
    | "none,left,down,right,up"
    | "none,left,down,up,right"
    | "none,down,left"
    | "none,up,left"
    | "none,up,left,down"
    | "none,up,down,left"
    | "none,down,left,up"
    | "none,down,up,left"
    | "none,right,left"
    | "none,right,left,up"
    | "none,right,left,down"
    | "none,right,left,up,down"
    | "none,right,left,down,up"
    | "none,right,down,left"
    | "none,right,up,left"
    | "none,right,up,left,down"
    | "none,right,up,down,left"
    | "none,right,down,left,up"
    | "none,right,down,up,left"
    | "none,down,left,right"
    | "none,down,right,left"
    | "none,up,left,right"
    | "none,up,left,right,down"
    | "none,up,left,down,right"
    | "none,up,right,left"
    | "none,up,right,left,down"
    | "none,up,right,down,left"
    | "none,up,down,left,right"
    | "none,up,down,right,left"
    | "none,down,left,right,up"
    | "none,down,left,up,right"
    | "none,down,right,left,up"
    | "none,down,right,up,left"
    | "none,down,up,left,right"
    | "none,down,up,right,left"
    | "none,ambiguous,left"
    | "none,ambiguous,right"
    | "none,ambiguous,up"
    | "none,ambiguous,down"
    | "none,ambiguous,up,down"
    | "none,ambiguous,down,up"
    | "none,ambiguous,right,up"
    | "none,ambiguous,right,down"
    | "none,ambiguous,right,up,down"
    | "none,ambiguous,right,down,up"
    | "none,ambiguous,down,right"
    | "none,ambiguous,up,right"
    | "none,ambiguous,up,right,down"
    | "none,ambiguous,up,down,right"
    | "none,ambiguous,down,right,up"
    | "none,ambiguous,down,up,right"
    | "none,ambiguous,left,right"
    | "none,ambiguous,left,up"
    | "none,ambiguous,left,down"
    | "none,ambiguous,left,up,down"
    | "none,ambiguous,left,down,up"
    | "none,ambiguous,left,right,up"
    | "none,ambiguous,left,right,down"
    | "none,ambiguous,left,right,up,down"
    | "none,ambiguous,left,right,down,up"
    | "none,ambiguous,left,down,right"
    | "none,ambiguous,left,up,right"
    | "none,ambiguous,left,up,right,down"
    | "none,ambiguous,left,up,down,right"
    | "none,ambiguous,left,down,right,up"
    | "none,ambiguous,left,down,up,right"
    | "none,ambiguous,down,left"
    | "none,ambiguous,up,left"
    | "none,ambiguous,up,left,down"
    | "none,ambiguous,up,down,left"
    | "none,ambiguous,down,left,up"
    | "none,ambiguous,down,up,left"
    | "none,ambiguous,right,left"
    | "none,ambiguous,right,left,up"
    | "none,ambiguous,right,left,down"
    | "none,ambiguous,right,left,up,down"
    | "none,ambiguous,right,left,down,up"
    | "none,ambiguous,right,down,left"
    | "none,ambiguous,right,up,left"
    | "none,ambiguous,right,up,left,down"
    | "none,ambiguous,right,up,down,left"
    | "none,ambiguous,right,down,left,up"
    | "none,ambiguous,right,down,up,left"
    | "none,ambiguous,down,left,right"
    | "none,ambiguous,down,right,left"
    | "none,ambiguous,up,left,right"
    | "none,ambiguous,up,left,right,down"
    | "none,ambiguous,up,left,down,right"
    | "none,ambiguous,up,right,left"
    | "none,ambiguous,up,right,left,down"
    | "none,ambiguous,up,right,down,left"
    | "none,ambiguous,up,down,left,right"
    | "none,ambiguous,up,down,right,left"
    | "none,ambiguous,down,left,right,up"
    | "none,ambiguous,down,left,up,right"
    | "none,ambiguous,down,right,left,up"
    | "none,ambiguous,down,right,up,left"
    | "none,ambiguous,down,up,left,right"
    | "none,ambiguous,down,up,right,left"
    | "none,down,ambiguous"
    | "none,up,ambiguous"
    | "none,up,ambiguous,down"
    | "none,up,down,ambiguous"
    | "none,down,ambiguous,up"
    | "none,down,up,ambiguous"
    | "none,right,ambiguous"
    | "none,right,ambiguous,up"
    | "none,right,ambiguous,down"
    | "none,right,ambiguous,up,down"
    | "none,right,ambiguous,down,up"
    | "none,right,down,ambiguous"
    | "none,right,up,ambiguous"
    | "none,right,up,ambiguous,down"
    | "none,right,up,down,ambiguous"
    | "none,right,down,ambiguous,up"
    | "none,right,down,up,ambiguous"
    | "none,down,ambiguous,right"
    | "none,down,right,ambiguous"
    | "none,up,ambiguous,right"
    | "none,up,ambiguous,right,down"
    | "none,up,ambiguous,down,right"
    | "none,up,right,ambiguous"
    | "none,up,right,ambiguous,down"
    | "none,up,right,down,ambiguous"
    | "none,up,down,ambiguous,right"
    | "none,up,down,right,ambiguous"
    | "none,down,ambiguous,right,up"
    | "none,down,ambiguous,up,right"
    | "none,down,right,ambiguous,up"
    | "none,down,right,up,ambiguous"
    | "none,down,up,ambiguous,right"
    | "none,down,up,right,ambiguous"
    | "none,left,ambiguous"
    | "none,left,ambiguous,right"
    | "none,left,ambiguous,up"
    | "none,left,ambiguous,down"
    | "none,left,ambiguous,up,down"
    | "none,left,ambiguous,down,up"
    | "none,left,ambiguous,right,up"
    | "none,left,ambiguous,right,down"
    | "none,left,ambiguous,right,up,down"
    | "none,left,ambiguous,right,down,up"
    | "none,left,ambiguous,down,right"
    | "none,left,ambiguous,up,right"
    | "none,left,ambiguous,up,right,down"
    | "none,left,ambiguous,up,down,right"
    | "none,left,ambiguous,down,right,up"
    | "none,left,ambiguous,down,up,right"
    | "none,left,down,ambiguous"
    | "none,left,up,ambiguous"
    | "none,left,up,ambiguous,down"
    | "none,left,up,down,ambiguous"
    | "none,left,down,ambiguous,up"
    | "none,left,down,up,ambiguous"
    | "none,left,right,ambiguous"
    | "none,left,right,ambiguous,up"
    | "none,left,right,ambiguous,down"
    | "none,left,right,ambiguous,up,down"
    | "none,left,right,ambiguous,down,up"
    | "none,left,right,down,ambiguous"
    | "none,left,right,up,ambiguous"
    | "none,left,right,up,ambiguous,down"
    | "none,left,right,up,down,ambiguous"
    | "none,left,right,down,ambiguous,up"
    | "none,left,right,down,up,ambiguous"
    | "none,left,down,ambiguous,right"
    | "none,left,down,right,ambiguous"
    | "none,left,up,ambiguous,right"
    | "none,left,up,ambiguous,right,down"
    | "none,left,up,ambiguous,down,right"
    | "none,left,up,right,ambiguous"
    | "none,left,up,right,ambiguous,down"
    | "none,left,up,right,down,ambiguous"
    | "none,left,up,down,ambiguous,right"
    | "none,left,up,down,right,ambiguous"
    | "none,left,down,ambiguous,right,up"
    | "none,left,down,ambiguous,up,right"
    | "none,left,down,right,ambiguous,up"
    | "none,left,down,right,up,ambiguous"
    | "none,left,down,up,ambiguous,right"
    | "none,left,down,up,right,ambiguous"
    | "none,down,ambiguous,left"
    | "none,down,left,ambiguous"
    | "none,up,ambiguous,left"
    | "none,up,ambiguous,left,down"
    | "none,up,ambiguous,down,left"
    | "none,up,left,ambiguous"
    | "none,up,left,ambiguous,down"
    | "none,up,left,down,ambiguous"
    | "none,up,down,ambiguous,left"
    | "none,up,down,left,ambiguous"
    | "none,down,ambiguous,left,up"
    | "none,down,ambiguous,up,left"
    | "none,down,left,ambiguous,up"
    | "none,down,left,up,ambiguous"
    | "none,down,up,ambiguous,left"
    | "none,down,up,left,ambiguous"
    | "none,right,ambiguous,left"
    | "none,right,ambiguous,left,up"
    | "none,right,ambiguous,left,down"
    | "none,right,ambiguous,left,up,down"
    | "none,right,ambiguous,left,down,up"
    | "none,right,ambiguous,down,left"
    | "none,right,ambiguous,up,left"
    | "none,right,ambiguous,up,left,down"
    | "none,right,ambiguous,up,down,left"
    | "none,right,ambiguous,down,left,up"
    | "none,right,ambiguous,down,up,left"
    | "none,right,left,ambiguous"
    | "none,right,left,ambiguous,up"
    | "none,right,left,ambiguous,down"
    | "none,right,left,ambiguous,up,down"
    | "none,right,left,ambiguous,down,up"
    | "none,right,left,down,ambiguous"
    | "none,right,left,up,ambiguous"
    | "none,right,left,up,ambiguous,down"
    | "none,right,left,up,down,ambiguous"
    | "none,right,left,down,ambiguous,up"
    | "none,right,left,down,up,ambiguous"
    | "none,right,down,ambiguous,left"
    | "none,right,down,left,ambiguous"
    | "none,right,up,ambiguous,left"
    | "none,right,up,ambiguous,left,down"
    | "none,right,up,ambiguous,down,left"
    | "none,right,up,left,ambiguous"
    | "none,right,up,left,ambiguous,down"
    | "none,right,up,left,down,ambiguous"
    | "none,right,up,down,ambiguous,left"
    | "none,right,up,down,left,ambiguous"
    | "none,right,down,ambiguous,left,up"
    | "none,right,down,ambiguous,up,left"
    | "none,right,down,left,ambiguous,up"
    | "none,right,down,left,up,ambiguous"
    | "none,right,down,up,ambiguous,left"
    | "none,right,down,up,left,ambiguous"
    | "none,down,ambiguous,left,right"
    | "none,down,ambiguous,right,left"
    | "none,down,left,ambiguous,right"
    | "none,down,left,right,ambiguous"
    | "none,down,right,ambiguous,left"
    | "none,down,right,left,ambiguous"
    | "none,up,ambiguous,left,right"
    | "none,up,ambiguous,left,right,down"
    | "none,up,ambiguous,left,down,right"
    | "none,up,ambiguous,right,left"
    | "none,up,ambiguous,right,left,down"
    | "none,up,ambiguous,right,down,left"
    | "none,up,ambiguous,down,left,right"
    | "none,up,ambiguous,down,right,left"
    | "none,up,left,ambiguous,right"
    | "none,up,left,ambiguous,right,down"
    | "none,up,left,ambiguous,down,right"
    | "none,up,left,right,ambiguous"
    | "none,up,left,right,ambiguous,down"
    | "none,up,left,right,down,ambiguous"
    | "none,up,left,down,ambiguous,right"
    | "none,up,left,down,right,ambiguous"
    | "none,up,right,ambiguous,left"
    | "none,up,right,ambiguous,left,down"
    | "none,up,right,ambiguous,down,left"
    | "none,up,right,left,ambiguous"
    | "none,up,right,left,ambiguous,down"
    | "none,up,right,left,down,ambiguous"
    | "none,up,right,down,ambiguous,left"
    | "none,up,right,down,left,ambiguous"
    | "none,up,down,ambiguous,left,right"
    | "none,up,down,ambiguous,right,left"
    | "none,up,down,left,ambiguous,right"
    | "none,up,down,left,right,ambiguous"
    | "none,up,down,right,ambiguous,left"
    | "none,up,down,right,left,ambiguous"
    | "none,down,ambiguous,left,right,up"
    | "none,down,ambiguous,left,up,right"
    | "none,down,ambiguous,right,left,up"
    | "none,down,ambiguous,right,up,left"
    | "none,down,ambiguous,up,left,right"
    | "none,down,ambiguous,up,right,left"
    | "none,down,left,ambiguous,right,up"
    | "none,down,left,ambiguous,up,right"
    | "none,down,left,right,ambiguous,up"
    | "none,down,left,right,up,ambiguous"
    | "none,down,left,up,ambiguous,right"
    | "none,down,left,up,right,ambiguous"
    | "none,down,right,ambiguous,left,up"
    | "none,down,right,ambiguous,up,left"
    | "none,down,right,left,ambiguous,up"
    | "none,down,right,left,up,ambiguous"
    | "none,down,right,up,ambiguous,left"
    | "none,down,right,up,left,ambiguous"
    | "none,down,up,ambiguous,left,right"
    | "none,down,up,ambiguous,right,left"
    | "none,down,up,left,ambiguous,right"
    | "none,down,up,left,right,ambiguous"
    | "none,down,up,right,ambiguous,left"
    | "none,down,up,right,left,ambiguous"
    | "ambiguous,none"
    | "down,none"
    | "down,none,ambiguous"
    | "down,ambiguous,none"
    | "ambiguous,none,down"
    | "ambiguous,down,none"
    | "up,none"
    | "up,none,down"
    | "up,none,ambiguous"
    | "up,none,ambiguous,down"
    | "up,none,down,ambiguous"
    | "up,ambiguous,none"
    | "up,down,none"
    | "up,down,none,ambiguous"
    | "up,down,ambiguous,none"
    | "up,ambiguous,none,down"
    | "up,ambiguous,down,none"
    | "ambiguous,none,up"
    | "ambiguous,up,none"
    | "down,none,up"
    | "down,none,ambiguous,up"
    | "down,none,up,ambiguous"
    | "down,up,none"
    | "down,up,none,ambiguous"
    | "down,up,ambiguous,none"
    | "down,ambiguous,none,up"
    | "down,ambiguous,up,none"
    | "ambiguous,none,up,down"
    | "ambiguous,none,down,up"
    | "ambiguous,up,none,down"
    | "ambiguous,up,down,none"
    | "ambiguous,down,none,up"
    | "ambiguous,down,up,none"
    | "right,none"
    | "right,none,up"
    | "right,none,down"
    | "right,none,ambiguous"
    | "right,none,up,down"
    | "right,none,down,up"
    | "right,none,ambiguous,up"
    | "right,none,ambiguous,down"
    | "right,none,ambiguous,up,down"
    | "right,none,ambiguous,down,up"
    | "right,none,down,ambiguous"
    | "right,none,up,ambiguous"
    | "right,none,up,ambiguous,down"
    | "right,none,up,down,ambiguous"
    | "right,none,down,ambiguous,up"
    | "right,none,down,up,ambiguous"
    | "right,ambiguous,none"
    | "right,down,none"
    | "right,down,none,ambiguous"
    | "right,down,ambiguous,none"
    | "right,ambiguous,none,down"
    | "right,ambiguous,down,none"
    | "right,up,none"
    | "right,up,none,down"
    | "right,up,none,ambiguous"
    | "right,up,none,ambiguous,down"
    | "right,up,none,down,ambiguous"
    | "right,up,ambiguous,none"
    | "right,up,down,none"
    | "right,up,down,none,ambiguous"
    | "right,up,down,ambiguous,none"
    | "right,up,ambiguous,none,down"
    | "right,up,ambiguous,down,none"
    | "right,ambiguous,none,up"
    | "right,ambiguous,up,none"
    | "right,down,none,up"
    | "right,down,none,ambiguous,up"
    | "right,down,none,up,ambiguous"
    | "right,down,up,none"
    | "right,down,up,none,ambiguous"
    | "right,down,up,ambiguous,none"
    | "right,down,ambiguous,none,up"
    | "right,down,ambiguous,up,none"
    | "right,ambiguous,none,up,down"
    | "right,ambiguous,none,down,up"
    | "right,ambiguous,up,none,down"
    | "right,ambiguous,up,down,none"
    | "right,ambiguous,down,none,up"
    | "right,ambiguous,down,up,none"
    | "ambiguous,none,right"
    | "ambiguous,right,none"
    | "down,none,right"
    | "down,none,ambiguous,right"
    | "down,none,right,ambiguous"
    | "down,right,none"
    | "down,right,none,ambiguous"
    | "down,right,ambiguous,none"
    | "down,ambiguous,none,right"
    | "down,ambiguous,right,none"
    | "ambiguous,none,right,down"
    | "ambiguous,none,down,right"
    | "ambiguous,right,none,down"
    | "ambiguous,right,down,none"
    | "ambiguous,down,none,right"
    | "ambiguous,down,right,none"
    | "up,none,right"
    | "up,none,right,down"
    | "up,none,down,right"
    | "up,none,ambiguous,right"
    | "up,none,ambiguous,right,down"
    | "up,none,ambiguous,down,right"
    | "up,none,right,ambiguous"
    | "up,none,right,ambiguous,down"
    | "up,none,right,down,ambiguous"
    | "up,none,down,ambiguous,right"
    | "up,none,down,right,ambiguous"
    | "up,right,none"
    | "up,right,none,down"
    | "up,right,none,ambiguous"
    | "up,right,none,ambiguous,down"
    | "up,right,none,down,ambiguous"
    | "up,right,ambiguous,none"
    | "up,right,down,none"
    | "up,right,down,none,ambiguous"
    | "up,right,down,ambiguous,none"
    | "up,right,ambiguous,none,down"
    | "up,right,ambiguous,down,none"
    | "up,ambiguous,none,right"
    | "up,ambiguous,right,none"
    | "up,down,none,right"
    | "up,down,none,ambiguous,right"
    | "up,down,none,right,ambiguous"
    | "up,down,right,none"
    | "up,down,right,none,ambiguous"
    | "up,down,right,ambiguous,none"
    | "up,down,ambiguous,none,right"
    | "up,down,ambiguous,right,none"
    | "up,ambiguous,none,right,down"
    | "up,ambiguous,none,down,right"
    | "up,ambiguous,right,none,down"
    | "up,ambiguous,right,down,none"
    | "up,ambiguous,down,none,right"
    | "up,ambiguous,down,right,none"
    | "ambiguous,none,right,up"
    | "ambiguous,none,up,right"
    | "ambiguous,right,none,up"
    | "ambiguous,right,up,none"
    | "ambiguous,up,none,right"
    | "ambiguous,up,right,none"
    | "down,none,right,up"
    | "down,none,up,right"
    | "down,none,ambiguous,right,up"
    | "down,none,ambiguous,up,right"
    | "down,none,right,ambiguous,up"
    | "down,none,right,up,ambiguous"
    | "down,none,up,ambiguous,right"
    | "down,none,up,right,ambiguous"
    | "down,right,none,up"
    | "down,right,none,ambiguous,up"
    | "down,right,none,up,ambiguous"
    | "down,right,up,none"
    | "down,right,up,none,ambiguous"
    | "down,right,up,ambiguous,none"
    | "down,right,ambiguous,none,up"
    | "down,right,ambiguous,up,none"
    | "down,up,none,right"
    | "down,up,none,ambiguous,right"
    | "down,up,none,right,ambiguous"
    | "down,up,right,none"
    | "down,up,right,none,ambiguous"
    | "down,up,right,ambiguous,none"
    | "down,up,ambiguous,none,right"
    | "down,up,ambiguous,right,none"
    | "down,ambiguous,none,right,up"
    | "down,ambiguous,none,up,right"
    | "down,ambiguous,right,none,up"
    | "down,ambiguous,right,up,none"
    | "down,ambiguous,up,none,right"
    | "down,ambiguous,up,right,none"
    | "ambiguous,none,right,up,down"
    | "ambiguous,none,right,down,up"
    | "ambiguous,none,up,right,down"
    | "ambiguous,none,up,down,right"
    | "ambiguous,none,down,right,up"
    | "ambiguous,none,down,up,right"
    | "ambiguous,right,none,up,down"
    | "ambiguous,right,none,down,up"
    | "ambiguous,right,up,none,down"
    | "ambiguous,right,up,down,none"
    | "ambiguous,right,down,none,up"
    | "ambiguous,right,down,up,none"
    | "ambiguous,up,none,right,down"
    | "ambiguous,up,none,down,right"
    | "ambiguous,up,right,none,down"
    | "ambiguous,up,right,down,none"
    | "ambiguous,up,down,none,right"
    | "ambiguous,up,down,right,none"
    | "ambiguous,down,none,right,up"
    | "ambiguous,down,none,up,right"
    | "ambiguous,down,right,none,up"
    | "ambiguous,down,right,up,none"
    | "ambiguous,down,up,none,right"
    | "ambiguous,down,up,right,none"
    | "left,none"
    | "left,none,right"
    | "left,none,up"
    | "left,none,down"
    | "left,none,ambiguous"
    | "left,none,up,down"
    | "left,none,down,up"
    | "left,none,right,up"
    | "left,none,right,down"
    | "left,none,right,up,down"
    | "left,none,right,down,up"
    | "left,none,down,right"
    | "left,none,up,right"
    | "left,none,up,right,down"
    | "left,none,up,down,right"
    | "left,none,down,right,up"
    | "left,none,down,up,right"
    | "left,none,ambiguous,right"
    | "left,none,ambiguous,up"
    | "left,none,ambiguous,down"
    | "left,none,ambiguous,up,down"
    | "left,none,ambiguous,down,up"
    | "left,none,ambiguous,right,up"
    | "left,none,ambiguous,right,down"
    | "left,none,ambiguous,right,up,down"
    | "left,none,ambiguous,right,down,up"
    | "left,none,ambiguous,down,right"
    | "left,none,ambiguous,up,right"
    | "left,none,ambiguous,up,right,down"
    | "left,none,ambiguous,up,down,right"
    | "left,none,ambiguous,down,right,up"
    | "left,none,ambiguous,down,up,right"
    | "left,none,down,ambiguous"
    | "left,none,up,ambiguous"
    | "left,none,up,ambiguous,down"
    | "left,none,up,down,ambiguous"
    | "left,none,down,ambiguous,up"
    | "left,none,down,up,ambiguous"
    | "left,none,right,ambiguous"
    | "left,none,right,ambiguous,up"
    | "left,none,right,ambiguous,down"
    | "left,none,right,ambiguous,up,down"
    | "left,none,right,ambiguous,down,up"
    | "left,none,right,down,ambiguous"
    | "left,none,right,up,ambiguous"
    | "left,none,right,up,ambiguous,down"
    | "left,none,right,up,down,ambiguous"
    | "left,none,right,down,ambiguous,up"
    | "left,none,right,down,up,ambiguous"
    | "left,none,down,ambiguous,right"
    | "left,none,down,right,ambiguous"
    | "left,none,up,ambiguous,right"
    | "left,none,up,ambiguous,right,down"
    | "left,none,up,ambiguous,down,right"
    | "left,none,up,right,ambiguous"
    | "left,none,up,right,ambiguous,down"
    | "left,none,up,right,down,ambiguous"
    | "left,none,up,down,ambiguous,right"
    | "left,none,up,down,right,ambiguous"
    | "left,none,down,ambiguous,right,up"
    | "left,none,down,ambiguous,up,right"
    | "left,none,down,right,ambiguous,up"
    | "left,none,down,right,up,ambiguous"
    | "left,none,down,up,ambiguous,right"
    | "left,none,down,up,right,ambiguous"
    | "left,ambiguous,none"
    | "left,down,none"
    | "left,down,none,ambiguous"
    | "left,down,ambiguous,none"
    | "left,ambiguous,none,down"
    | "left,ambiguous,down,none"
    | "left,up,none"
    | "left,up,none,down"
    | "left,up,none,ambiguous"
    | "left,up,none,ambiguous,down"
    | "left,up,none,down,ambiguous"
    | "left,up,ambiguous,none"
    | "left,up,down,none"
    | "left,up,down,none,ambiguous"
    | "left,up,down,ambiguous,none"
    | "left,up,ambiguous,none,down"
    | "left,up,ambiguous,down,none"
    | "left,ambiguous,none,up"
    | "left,ambiguous,up,none"
    | "left,down,none,up"
    | "left,down,none,ambiguous,up"
    | "left,down,none,up,ambiguous"
    | "left,down,up,none"
    | "left,down,up,none,ambiguous"
    | "left,down,up,ambiguous,none"
    | "left,down,ambiguous,none,up"
    | "left,down,ambiguous,up,none"
    | "left,ambiguous,none,up,down"
    | "left,ambiguous,none,down,up"
    | "left,ambiguous,up,none,down"
    | "left,ambiguous,up,down,none"
    | "left,ambiguous,down,none,up"
    | "left,ambiguous,down,up,none"
    | "left,right,none"
    | "left,right,none,up"
    | "left,right,none,down"
    | "left,right,none,ambiguous"
    | "left,right,none,up,down"
    | "left,right,none,down,up"
    | "left,right,none,ambiguous,up"
    | "left,right,none,ambiguous,down"
    | "left,right,none,ambiguous,up,down"
    | "left,right,none,ambiguous,down,up"
    | "left,right,none,down,ambiguous"
    | "left,right,none,up,ambiguous"
    | "left,right,none,up,ambiguous,down"
    | "left,right,none,up,down,ambiguous"
    | "left,right,none,down,ambiguous,up"
    | "left,right,none,down,up,ambiguous"
    | "left,right,ambiguous,none"
    | "left,right,down,none"
    | "left,right,down,none,ambiguous"
    | "left,right,down,ambiguous,none"
    | "left,right,ambiguous,none,down"
    | "left,right,ambiguous,down,none"
    | "left,right,up,none"
    | "left,right,up,none,down"
    | "left,right,up,none,ambiguous"
    | "left,right,up,none,ambiguous,down"
    | "left,right,up,none,down,ambiguous"
    | "left,right,up,ambiguous,none"
    | "left,right,up,down,none"
    | "left,right,up,down,none,ambiguous"
    | "left,right,up,down,ambiguous,none"
    | "left,right,up,ambiguous,none,down"
    | "left,right,up,ambiguous,down,none"
    | "left,right,ambiguous,none,up"
    | "left,right,ambiguous,up,none"
    | "left,right,down,none,up"
    | "left,right,down,none,ambiguous,up"
    | "left,right,down,none,up,ambiguous"
    | "left,right,down,up,none"
    | "left,right,down,up,none,ambiguous"
    | "left,right,down,up,ambiguous,none"
    | "left,right,down,ambiguous,none,up"
    | "left,right,down,ambiguous,up,none"
    | "left,right,ambiguous,none,up,down"
    | "left,right,ambiguous,none,down,up"
    | "left,right,ambiguous,up,none,down"
    | "left,right,ambiguous,up,down,none"
    | "left,right,ambiguous,down,none,up"
    | "left,right,ambiguous,down,up,none"
    | "left,ambiguous,none,right"
    | "left,ambiguous,right,none"
    | "left,down,none,right"
    | "left,down,none,ambiguous,right"
    | "left,down,none,right,ambiguous"
    | "left,down,right,none"
    | "left,down,right,none,ambiguous"
    | "left,down,right,ambiguous,none"
    | "left,down,ambiguous,none,right"
    | "left,down,ambiguous,right,none"
    | "left,ambiguous,none,right,down"
    | "left,ambiguous,none,down,right"
    | "left,ambiguous,right,none,down"
    | "left,ambiguous,right,down,none"
    | "left,ambiguous,down,none,right"
    | "left,ambiguous,down,right,none"
    | "left,up,none,right"
    | "left,up,none,right,down"
    | "left,up,none,down,right"
    | "left,up,none,ambiguous,right"
    | "left,up,none,ambiguous,right,down"
    | "left,up,none,ambiguous,down,right"
    | "left,up,none,right,ambiguous"
    | "left,up,none,right,ambiguous,down"
    | "left,up,none,right,down,ambiguous"
    | "left,up,none,down,ambiguous,right"
    | "left,up,none,down,right,ambiguous"
    | "left,up,right,none"
    | "left,up,right,none,down"
    | "left,up,right,none,ambiguous"
    | "left,up,right,none,ambiguous,down"
    | "left,up,right,none,down,ambiguous"
    | "left,up,right,ambiguous,none"
    | "left,up,right,down,none"
    | "left,up,right,down,none,ambiguous"
    | "left,up,right,down,ambiguous,none"
    | "left,up,right,ambiguous,none,down"
    | "left,up,right,ambiguous,down,none"
    | "left,up,ambiguous,none,right"
    | "left,up,ambiguous,right,none"
    | "left,up,down,none,right"
    | "left,up,down,none,ambiguous,right"
    | "left,up,down,none,right,ambiguous"
    | "left,up,down,right,none"
    | "left,up,down,right,none,ambiguous"
    | "left,up,down,right,ambiguous,none"
    | "left,up,down,ambiguous,none,right"
    | "left,up,down,ambiguous,right,none"
    | "left,up,ambiguous,none,right,down"
    | "left,up,ambiguous,none,down,right"
    | "left,up,ambiguous,right,none,down"
    | "left,up,ambiguous,right,down,none"
    | "left,up,ambiguous,down,none,right"
    | "left,up,ambiguous,down,right,none"
    | "left,ambiguous,none,right,up"
    | "left,ambiguous,none,up,right"
    | "left,ambiguous,right,none,up"
    | "left,ambiguous,right,up,none"
    | "left,ambiguous,up,none,right"
    | "left,ambiguous,up,right,none"
    | "left,down,none,right,up"
    | "left,down,none,up,right"
    | "left,down,none,ambiguous,right,up"
    | "left,down,none,ambiguous,up,right"
    | "left,down,none,right,ambiguous,up"
    | "left,down,none,right,up,ambiguous"
    | "left,down,none,up,ambiguous,right"
    | "left,down,none,up,right,ambiguous"
    | "left,down,right,none,up"
    | "left,down,right,none,ambiguous,up"
    | "left,down,right,none,up,ambiguous"
    | "left,down,right,up,none"
    | "left,down,right,up,none,ambiguous"
    | "left,down,right,up,ambiguous,none"
    | "left,down,right,ambiguous,none,up"
    | "left,down,right,ambiguous,up,none"
    | "left,down,up,none,right"
    | "left,down,up,none,ambiguous,right"
    | "left,down,up,none,right,ambiguous"
    | "left,down,up,right,none"
    | "left,down,up,right,none,ambiguous"
    | "left,down,up,right,ambiguous,none"
    | "left,down,up,ambiguous,none,right"
    | "left,down,up,ambiguous,right,none"
    | "left,down,ambiguous,none,right,up"
    | "left,down,ambiguous,none,up,right"
    | "left,down,ambiguous,right,none,up"
    | "left,down,ambiguous,right,up,none"
    | "left,down,ambiguous,up,none,right"
    | "left,down,ambiguous,up,right,none"
    | "left,ambiguous,none,right,up,down"
    | "left,ambiguous,none,right,down,up"
    | "left,ambiguous,none,up,right,down"
    | "left,ambiguous,none,up,down,right"
    | "left,ambiguous,none,down,right,up"
    | "left,ambiguous,none,down,up,right"
    | "left,ambiguous,right,none,up,down"
    | "left,ambiguous,right,none,down,up"
    | "left,ambiguous,right,up,none,down"
    | "left,ambiguous,right,up,down,none"
    | "left,ambiguous,right,down,none,up"
    | "left,ambiguous,right,down,up,none"
    | "left,ambiguous,up,none,right,down"
    | "left,ambiguous,up,none,down,right"
    | "left,ambiguous,up,right,none,down"
    | "left,ambiguous,up,right,down,none"
    | "left,ambiguous,up,down,none,right"
    | "left,ambiguous,up,down,right,none"
    | "left,ambiguous,down,none,right,up"
    | "left,ambiguous,down,none,up,right"
    | "left,ambiguous,down,right,none,up"
    | "left,ambiguous,down,right,up,none"
    | "left,ambiguous,down,up,none,right"
    | "left,ambiguous,down,up,right,none"
    | "ambiguous,none,left"
    | "ambiguous,left,none"
    | "down,none,left"
    | "down,none,ambiguous,left"
    | "down,none,left,ambiguous"
    | "down,left,none"
    | "down,left,none,ambiguous"
    | "down,left,ambiguous,none"
    | "down,ambiguous,none,left"
    | "down,ambiguous,left,none"
    | "ambiguous,none,left,down"
    | "ambiguous,none,down,left"
    | "ambiguous,left,none,down"
    | "ambiguous,left,down,none"
    | "ambiguous,down,none,left"
    | "ambiguous,down,left,none"
    | "up,none,left"
    | "up,none,left,down"
    | "up,none,down,left"
    | "up,none,ambiguous,left"
    | "up,none,ambiguous,left,down"
    | "up,none,ambiguous,down,left"
    | "up,none,left,ambiguous"
    | "up,none,left,ambiguous,down"
    | "up,none,left,down,ambiguous"
    | "up,none,down,ambiguous,left"
    | "up,none,down,left,ambiguous"
    | "up,left,none"
    | "up,left,none,down"
    | "up,left,none,ambiguous"
    | "up,left,none,ambiguous,down"
    | "up,left,none,down,ambiguous"
    | "up,left,ambiguous,none"
    | "up,left,down,none"
    | "up,left,down,none,ambiguous"
    | "up,left,down,ambiguous,none"
    | "up,left,ambiguous,none,down"
    | "up,left,ambiguous,down,none"
    | "up,ambiguous,none,left"
    | "up,ambiguous,left,none"
    | "up,down,none,left"
    | "up,down,none,ambiguous,left"
    | "up,down,none,left,ambiguous"
    | "up,down,left,none"
    | "up,down,left,none,ambiguous"
    | "up,down,left,ambiguous,none"
    | "up,down,ambiguous,none,left"
    | "up,down,ambiguous,left,none"
    | "up,ambiguous,none,left,down"
    | "up,ambiguous,none,down,left"
    | "up,ambiguous,left,none,down"
    | "up,ambiguous,left,down,none"
    | "up,ambiguous,down,none,left"
    | "up,ambiguous,down,left,none"
    | "ambiguous,none,left,up"
    | "ambiguous,none,up,left"
    | "ambiguous,left,none,up"
    | "ambiguous,left,up,none"
    | "ambiguous,up,none,left"
    | "ambiguous,up,left,none"
    | "down,none,left,up"
    | "down,none,up,left"
    | "down,none,ambiguous,left,up"
    | "down,none,ambiguous,up,left"
    | "down,none,left,ambiguous,up"
    | "down,none,left,up,ambiguous"
    | "down,none,up,ambiguous,left"
    | "down,none,up,left,ambiguous"
    | "down,left,none,up"
    | "down,left,none,ambiguous,up"
    | "down,left,none,up,ambiguous"
    | "down,left,up,none"
    | "down,left,up,none,ambiguous"
    | "down,left,up,ambiguous,none"
    | "down,left,ambiguous,none,up"
    | "down,left,ambiguous,up,none"
    | "down,up,none,left"
    | "down,up,none,ambiguous,left"
    | "down,up,none,left,ambiguous"
    | "down,up,left,none"
    | "down,up,left,none,ambiguous"
    | "down,up,left,ambiguous,none"
    | "down,up,ambiguous,none,left"
    | "down,up,ambiguous,left,none"
    | "down,ambiguous,none,left,up"
    | "down,ambiguous,none,up,left"
    | "down,ambiguous,left,none,up"
    | "down,ambiguous,left,up,none"
    | "down,ambiguous,up,none,left"
    | "down,ambiguous,up,left,none"
    | "ambiguous,none,left,up,down"
    | "ambiguous,none,left,down,up"
    | "ambiguous,none,up,left,down"
    | "ambiguous,none,up,down,left"
    | "ambiguous,none,down,left,up"
    | "ambiguous,none,down,up,left"
    | "ambiguous,left,none,up,down"
    | "ambiguous,left,none,down,up"
    | "ambiguous,left,up,none,down"
    | "ambiguous,left,up,down,none"
    | "ambiguous,left,down,none,up"
    | "ambiguous,left,down,up,none"
    | "ambiguous,up,none,left,down"
    | "ambiguous,up,none,down,left"
    | "ambiguous,up,left,none,down"
    | "ambiguous,up,left,down,none"
    | "ambiguous,up,down,none,left"
    | "ambiguous,up,down,left,none"
    | "ambiguous,down,none,left,up"
    | "ambiguous,down,none,up,left"
    | "ambiguous,down,left,none,up"
    | "ambiguous,down,left,up,none"
    | "ambiguous,down,up,none,left"
    | "ambiguous,down,up,left,none"
    | "right,none,left"
    | "right,none,left,up"
    | "right,none,left,down"
    | "right,none,left,up,down"
    | "right,none,left,down,up"
    | "right,none,down,left"
    | "right,none,up,left"
    | "right,none,up,left,down"
    | "right,none,up,down,left"
    | "right,none,down,left,up"
    | "right,none,down,up,left"
    | "right,none,ambiguous,left"
    | "right,none,ambiguous,left,up"
    | "right,none,ambiguous,left,down"
    | "right,none,ambiguous,left,up,down"
    | "right,none,ambiguous,left,down,up"
    | "right,none,ambiguous,down,left"
    | "right,none,ambiguous,up,left"
    | "right,none,ambiguous,up,left,down"
    | "right,none,ambiguous,up,down,left"
    | "right,none,ambiguous,down,left,up"
    | "right,none,ambiguous,down,up,left"
    | "right,none,left,ambiguous"
    | "right,none,left,ambiguous,up"
    | "right,none,left,ambiguous,down"
    | "right,none,left,ambiguous,up,down"
    | "right,none,left,ambiguous,down,up"
    | "right,none,left,down,ambiguous"
    | "right,none,left,up,ambiguous"
    | "right,none,left,up,ambiguous,down"
    | "right,none,left,up,down,ambiguous"
    | "right,none,left,down,ambiguous,up"
    | "right,none,left,down,up,ambiguous"
    | "right,none,down,ambiguous,left"
    | "right,none,down,left,ambiguous"
    | "right,none,up,ambiguous,left"
    | "right,none,up,ambiguous,left,down"
    | "right,none,up,ambiguous,down,left"
    | "right,none,up,left,ambiguous"
    | "right,none,up,left,ambiguous,down"
    | "right,none,up,left,down,ambiguous"
    | "right,none,up,down,ambiguous,left"
    | "right,none,up,down,left,ambiguous"
    | "right,none,down,ambiguous,left,up"
    | "right,none,down,ambiguous,up,left"
    | "right,none,down,left,ambiguous,up"
    | "right,none,down,left,up,ambiguous"
    | "right,none,down,up,ambiguous,left"
    | "right,none,down,up,left,ambiguous"
    | "right,left,none"
    | "right,left,none,up"
    | "right,left,none,down"
    | "right,left,none,ambiguous"
    | "right,left,none,up,down"
    | "right,left,none,down,up"
    | "right,left,none,ambiguous,up"
    | "right,left,none,ambiguous,down"
    | "right,left,none,ambiguous,up,down"
    | "right,left,none,ambiguous,down,up"
    | "right,left,none,down,ambiguous"
    | "right,left,none,up,ambiguous"
    | "right,left,none,up,ambiguous,down"
    | "right,left,none,up,down,ambiguous"
    | "right,left,none,down,ambiguous,up"
    | "right,left,none,down,up,ambiguous"
    | "right,left,ambiguous,none"
    | "right,left,down,none"
    | "right,left,down,none,ambiguous"
    | "right,left,down,ambiguous,none"
    | "right,left,ambiguous,none,down"
    | "right,left,ambiguous,down,none"
    | "right,left,up,none"
    | "right,left,up,none,down"
    | "right,left,up,none,ambiguous"
    | "right,left,up,none,ambiguous,down"
    | "right,left,up,none,down,ambiguous"
    | "right,left,up,ambiguous,none"
    | "right,left,up,down,none"
    | "right,left,up,down,none,ambiguous"
    | "right,left,up,down,ambiguous,none"
    | "right,left,up,ambiguous,none,down"
    | "right,left,up,ambiguous,down,none"
    | "right,left,ambiguous,none,up"
    | "right,left,ambiguous,up,none"
    | "right,left,down,none,up"
    | "right,left,down,none,ambiguous,up"
    | "right,left,down,none,up,ambiguous"
    | "right,left,down,up,none"
    | "right,left,down,up,none,ambiguous"
    | "right,left,down,up,ambiguous,none"
    | "right,left,down,ambiguous,none,up"
    | "right,left,down,ambiguous,up,none"
    | "right,left,ambiguous,none,up,down"
    | "right,left,ambiguous,none,down,up"
    | "right,left,ambiguous,up,none,down"
    | "right,left,ambiguous,up,down,none"
    | "right,left,ambiguous,down,none,up"
    | "right,left,ambiguous,down,up,none"
    | "right,ambiguous,none,left"
    | "right,ambiguous,left,none"
    | "right,down,none,left"
    | "right,down,none,ambiguous,left"
    | "right,down,none,left,ambiguous"
    | "right,down,left,none"
    | "right,down,left,none,ambiguous"
    | "right,down,left,ambiguous,none"
    | "right,down,ambiguous,none,left"
    | "right,down,ambiguous,left,none"
    | "right,ambiguous,none,left,down"
    | "right,ambiguous,none,down,left"
    | "right,ambiguous,left,none,down"
    | "right,ambiguous,left,down,none"
    | "right,ambiguous,down,none,left"
    | "right,ambiguous,down,left,none"
    | "right,up,none,left"
    | "right,up,none,left,down"
    | "right,up,none,down,left"
    | "right,up,none,ambiguous,left"
    | "right,up,none,ambiguous,left,down"
    | "right,up,none,ambiguous,down,left"
    | "right,up,none,left,ambiguous"
    | "right,up,none,left,ambiguous,down"
    | "right,up,none,left,down,ambiguous"
    | "right,up,none,down,ambiguous,left"
    | "right,up,none,down,left,ambiguous"
    | "right,up,left,none"
    | "right,up,left,none,down"
    | "right,up,left,none,ambiguous"
    | "right,up,left,none,ambiguous,down"
    | "right,up,left,none,down,ambiguous"
    | "right,up,left,ambiguous,none"
    | "right,up,left,down,none"
    | "right,up,left,down,none,ambiguous"
    | "right,up,left,down,ambiguous,none"
    | "right,up,left,ambiguous,none,down"
    | "right,up,left,ambiguous,down,none"
    | "right,up,ambiguous,none,left"
    | "right,up,ambiguous,left,none"
    | "right,up,down,none,left"
    | "right,up,down,none,ambiguous,left"
    | "right,up,down,none,left,ambiguous"
    | "right,up,down,left,none"
    | "right,up,down,left,none,ambiguous"
    | "right,up,down,left,ambiguous,none"
    | "right,up,down,ambiguous,none,left"
    | "right,up,down,ambiguous,left,none"
    | "right,up,ambiguous,none,left,down"
    | "right,up,ambiguous,none,down,left"
    | "right,up,ambiguous,left,none,down"
    | "right,up,ambiguous,left,down,none"
    | "right,up,ambiguous,down,none,left"
    | "right,up,ambiguous,down,left,none"
    | "right,ambiguous,none,left,up"
    | "right,ambiguous,none,up,left"
    | "right,ambiguous,left,none,up"
    | "right,ambiguous,left,up,none"
    | "right,ambiguous,up,none,left"
    | "right,ambiguous,up,left,none"
    | "right,down,none,left,up"
    | "right,down,none,up,left"
    | "right,down,none,ambiguous,left,up"
    | "right,down,none,ambiguous,up,left"
    | "right,down,none,left,ambiguous,up"
    | "right,down,none,left,up,ambiguous"
    | "right,down,none,up,ambiguous,left"
    | "right,down,none,up,left,ambiguous"
    | "right,down,left,none,up"
    | "right,down,left,none,ambiguous,up"
    | "right,down,left,none,up,ambiguous"
    | "right,down,left,up,none"
    | "right,down,left,up,none,ambiguous"
    | "right,down,left,up,ambiguous,none"
    | "right,down,left,ambiguous,none,up"
    | "right,down,left,ambiguous,up,none"
    | "right,down,up,none,left"
    | "right,down,up,none,ambiguous,left"
    | "right,down,up,none,left,ambiguous"
    | "right,down,up,left,none"
    | "right,down,up,left,none,ambiguous"
    | "right,down,up,left,ambiguous,none"
    | "right,down,up,ambiguous,none,left"
    | "right,down,up,ambiguous,left,none"
    | "right,down,ambiguous,none,left,up"
    | "right,down,ambiguous,none,up,left"
    | "right,down,ambiguous,left,none,up"
    | "right,down,ambiguous,left,up,none"
    | "right,down,ambiguous,up,none,left"
    | "right,down,ambiguous,up,left,none"
    | "right,ambiguous,none,left,up,down"
    | "right,ambiguous,none,left,down,up"
    | "right,ambiguous,none,up,left,down"
    | "right,ambiguous,none,up,down,left"
    | "right,ambiguous,none,down,left,up"
    | "right,ambiguous,none,down,up,left"
    | "right,ambiguous,left,none,up,down"
    | "right,ambiguous,left,none,down,up"
    | "right,ambiguous,left,up,none,down"
    | "right,ambiguous,left,up,down,none"
    | "right,ambiguous,left,down,none,up"
    | "right,ambiguous,left,down,up,none"
    | "right,ambiguous,up,none,left,down"
    | "right,ambiguous,up,none,down,left"
    | "right,ambiguous,up,left,none,down"
    | "right,ambiguous,up,left,down,none"
    | "right,ambiguous,up,down,none,left"
    | "right,ambiguous,up,down,left,none"
    | "right,ambiguous,down,none,left,up"
    | "right,ambiguous,down,none,up,left"
    | "right,ambiguous,down,left,none,up"
    | "right,ambiguous,down,left,up,none"
    | "right,ambiguous,down,up,none,left"
    | "right,ambiguous,down,up,left,none"
    | "ambiguous,none,left,right"
    | "ambiguous,none,right,left"
    | "ambiguous,left,none,right"
    | "ambiguous,left,right,none"
    | "ambiguous,right,none,left"
    | "ambiguous,right,left,none"
    | "down,none,left,right"
    | "down,none,right,left"
    | "down,none,ambiguous,left,right"
    | "down,none,ambiguous,right,left"
    | "down,none,left,ambiguous,right"
    | "down,none,left,right,ambiguous"
    | "down,none,right,ambiguous,left"
    | "down,none,right,left,ambiguous"
    | "down,left,none,right"
    | "down,left,none,ambiguous,right"
    | "down,left,none,right,ambiguous"
    | "down,left,right,none"
    | "down,left,right,none,ambiguous"
    | "down,left,right,ambiguous,none"
    | "down,left,ambiguous,none,right"
    | "down,left,ambiguous,right,none"
    | "down,right,none,left"
    | "down,right,none,ambiguous,left"
    | "down,right,none,left,ambiguous"
    | "down,right,left,none"
    | "down,right,left,none,ambiguous"
    | "down,right,left,ambiguous,none"
    | "down,right,ambiguous,none,left"
    | "down,right,ambiguous,left,none"
    | "down,ambiguous,none,left,right"
    | "down,ambiguous,none,right,left"
    | "down,ambiguous,left,none,right"
    | "down,ambiguous,left,right,none"
    | "down,ambiguous,right,none,left"
    | "down,ambiguous,right,left,none"
    | "ambiguous,none,left,right,down"
    | "ambiguous,none,left,down,right"
    | "ambiguous,none,right,left,down"
    | "ambiguous,none,right,down,left"
    | "ambiguous,none,down,left,right"
    | "ambiguous,none,down,right,left"
    | "ambiguous,left,none,right,down"
    | "ambiguous,left,none,down,right"
    | "ambiguous,left,right,none,down"
    | "ambiguous,left,right,down,none"
    | "ambiguous,left,down,none,right"
    | "ambiguous,left,down,right,none"
    | "ambiguous,right,none,left,down"
    | "ambiguous,right,none,down,left"
    | "ambiguous,right,left,none,down"
    | "ambiguous,right,left,down,none"
    | "ambiguous,right,down,none,left"
    | "ambiguous,right,down,left,none"
    | "ambiguous,down,none,left,right"
    | "ambiguous,down,none,right,left"
    | "ambiguous,down,left,none,right"
    | "ambiguous,down,left,right,none"
    | "ambiguous,down,right,none,left"
    | "ambiguous,down,right,left,none"
    | "up,none,left,right"
    | "up,none,left,right,down"
    | "up,none,left,down,right"
    | "up,none,right,left"
    | "up,none,right,left,down"
    | "up,none,right,down,left"
    | "up,none,down,left,right"
    | "up,none,down,right,left"
    | "up,none,ambiguous,left,right"
    | "up,none,ambiguous,left,right,down"
    | "up,none,ambiguous,left,down,right"
    | "up,none,ambiguous,right,left"
    | "up,none,ambiguous,right,left,down"
    | "up,none,ambiguous,right,down,left"
    | "up,none,ambiguous,down,left,right"
    | "up,none,ambiguous,down,right,left"
    | "up,none,left,ambiguous,right"
    | "up,none,left,ambiguous,right,down"
    | "up,none,left,ambiguous,down,right"
    | "up,none,left,right,ambiguous"
    | "up,none,left,right,ambiguous,down"
    | "up,none,left,right,down,ambiguous"
    | "up,none,left,down,ambiguous,right"
    | "up,none,left,down,right,ambiguous"
    | "up,none,right,ambiguous,left"
    | "up,none,right,ambiguous,left,down"
    | "up,none,right,ambiguous,down,left"
    | "up,none,right,left,ambiguous"
    | "up,none,right,left,ambiguous,down"
    | "up,none,right,left,down,ambiguous"
    | "up,none,right,down,ambiguous,left"
    | "up,none,right,down,left,ambiguous"
    | "up,none,down,ambiguous,left,right"
    | "up,none,down,ambiguous,right,left"
    | "up,none,down,left,ambiguous,right"
    | "up,none,down,left,right,ambiguous"
    | "up,none,down,right,ambiguous,left"
    | "up,none,down,right,left,ambiguous"
    | "up,left,none,right"
    | "up,left,none,right,down"
    | "up,left,none,down,right"
    | "up,left,none,ambiguous,right"
    | "up,left,none,ambiguous,right,down"
    | "up,left,none,ambiguous,down,right"
    | "up,left,none,right,ambiguous"
    | "up,left,none,right,ambiguous,down"
    | "up,left,none,right,down,ambiguous"
    | "up,left,none,down,ambiguous,right"
    | "up,left,none,down,right,ambiguous"
    | "up,left,right,none"
    | "up,left,right,none,down"
    | "up,left,right,none,ambiguous"
    | "up,left,right,none,ambiguous,down"
    | "up,left,right,none,down,ambiguous"
    | "up,left,right,ambiguous,none"
    | "up,left,right,down,none"
    | "up,left,right,down,none,ambiguous"
    | "up,left,right,down,ambiguous,none"
    | "up,left,right,ambiguous,none,down"
    | "up,left,right,ambiguous,down,none"
    | "up,left,ambiguous,none,right"
    | "up,left,ambiguous,right,none"
    | "up,left,down,none,right"
    | "up,left,down,none,ambiguous,right"
    | "up,left,down,none,right,ambiguous"
    | "up,left,down,right,none"
    | "up,left,down,right,none,ambiguous"
    | "up,left,down,right,ambiguous,none"
    | "up,left,down,ambiguous,none,right"
    | "up,left,down,ambiguous,right,none"
    | "up,left,ambiguous,none,right,down"
    | "up,left,ambiguous,none,down,right"
    | "up,left,ambiguous,right,none,down"
    | "up,left,ambiguous,right,down,none"
    | "up,left,ambiguous,down,none,right"
    | "up,left,ambiguous,down,right,none"
    | "up,right,none,left"
    | "up,right,none,left,down"
    | "up,right,none,down,left"
    | "up,right,none,ambiguous,left"
    | "up,right,none,ambiguous,left,down"
    | "up,right,none,ambiguous,down,left"
    | "up,right,none,left,ambiguous"
    | "up,right,none,left,ambiguous,down"
    | "up,right,none,left,down,ambiguous"
    | "up,right,none,down,ambiguous,left"
    | "up,right,none,down,left,ambiguous"
    | "up,right,left,none"
    | "up,right,left,none,down"
    | "up,right,left,none,ambiguous"
    | "up,right,left,none,ambiguous,down"
    | "up,right,left,none,down,ambiguous"
    | "up,right,left,ambiguous,none"
    | "up,right,left,down,none"
    | "up,right,left,down,none,ambiguous"
    | "up,right,left,down,ambiguous,none"
    | "up,right,left,ambiguous,none,down"
    | "up,right,left,ambiguous,down,none"
    | "up,right,ambiguous,none,left"
    | "up,right,ambiguous,left,none"
    | "up,right,down,none,left"
    | "up,right,down,none,ambiguous,left"
    | "up,right,down,none,left,ambiguous"
    | "up,right,down,left,none"
    | "up,right,down,left,none,ambiguous"
    | "up,right,down,left,ambiguous,none"
    | "up,right,down,ambiguous,none,left"
    | "up,right,down,ambiguous,left,none"
    | "up,right,ambiguous,none,left,down"
    | "up,right,ambiguous,none,down,left"
    | "up,right,ambiguous,left,none,down"
    | "up,right,ambiguous,left,down,none"
    | "up,right,ambiguous,down,none,left"
    | "up,right,ambiguous,down,left,none"
    | "up,ambiguous,none,left,right"
    | "up,ambiguous,none,right,left"
    | "up,ambiguous,left,none,right"
    | "up,ambiguous,left,right,none"
    | "up,ambiguous,right,none,left"
    | "up,ambiguous,right,left,none"
    | "up,down,none,left,right"
    | "up,down,none,right,left"
    | "up,down,none,ambiguous,left,right"
    | "up,down,none,ambiguous,right,left"
    | "up,down,none,left,ambiguous,right"
    | "up,down,none,left,right,ambiguous"
    | "up,down,none,right,ambiguous,left"
    | "up,down,none,right,left,ambiguous"
    | "up,down,left,none,right"
    | "up,down,left,none,ambiguous,right"
    | "up,down,left,none,right,ambiguous"
    | "up,down,left,right,none"
    | "up,down,left,right,none,ambiguous"
    | "up,down,left,right,ambiguous,none"
    | "up,down,left,ambiguous,none,right"
    | "up,down,left,ambiguous,right,none"
    | "up,down,right,none,left"
    | "up,down,right,none,ambiguous,left"
    | "up,down,right,none,left,ambiguous"
    | "up,down,right,left,none"
    | "up,down,right,left,none,ambiguous"
    | "up,down,right,left,ambiguous,none"
    | "up,down,right,ambiguous,none,left"
    | "up,down,right,ambiguous,left,none"
    | "up,down,ambiguous,none,left,right"
    | "up,down,ambiguous,none,right,left"
    | "up,down,ambiguous,left,none,right"
    | "up,down,ambiguous,left,right,none"
    | "up,down,ambiguous,right,none,left"
    | "up,down,ambiguous,right,left,none"
    | "up,ambiguous,none,left,right,down"
    | "up,ambiguous,none,left,down,right"
    | "up,ambiguous,none,right,left,down"
    | "up,ambiguous,none,right,down,left"
    | "up,ambiguous,none,down,left,right"
    | "up,ambiguous,none,down,right,left"
    | "up,ambiguous,left,none,right,down"
    | "up,ambiguous,left,none,down,right"
    | "up,ambiguous,left,right,none,down"
    | "up,ambiguous,left,right,down,none"
    | "up,ambiguous,left,down,none,right"
    | "up,ambiguous,left,down,right,none"
    | "up,ambiguous,right,none,left,down"
    | "up,ambiguous,right,none,down,left"
    | "up,ambiguous,right,left,none,down"
    | "up,ambiguous,right,left,down,none"
    | "up,ambiguous,right,down,none,left"
    | "up,ambiguous,right,down,left,none"
    | "up,ambiguous,down,none,left,right"
    | "up,ambiguous,down,none,right,left"
    | "up,ambiguous,down,left,none,right"
    | "up,ambiguous,down,left,right,none"
    | "up,ambiguous,down,right,none,left"
    | "up,ambiguous,down,right,left,none"
    | "ambiguous,none,left,right,up"
    | "ambiguous,none,left,up,right"
    | "ambiguous,none,right,left,up"
    | "ambiguous,none,right,up,left"
    | "ambiguous,none,up,left,right"
    | "ambiguous,none,up,right,left"
    | "ambiguous,left,none,right,up"
    | "ambiguous,left,none,up,right"
    | "ambiguous,left,right,none,up"
    | "ambiguous,left,right,up,none"
    | "ambiguous,left,up,none,right"
    | "ambiguous,left,up,right,none"
    | "ambiguous,right,none,left,up"
    | "ambiguous,right,none,up,left"
    | "ambiguous,right,left,none,up"
    | "ambiguous,right,left,up,none"
    | "ambiguous,right,up,none,left"
    | "ambiguous,right,up,left,none"
    | "ambiguous,up,none,left,right"
    | "ambiguous,up,none,right,left"
    | "ambiguous,up,left,none,right"
    | "ambiguous,up,left,right,none"
    | "ambiguous,up,right,none,left"
    | "ambiguous,up,right,left,none"
    | "down,none,left,right,up"
    | "down,none,left,up,right"
    | "down,none,right,left,up"
    | "down,none,right,up,left"
    | "down,none,up,left,right"
    | "down,none,up,right,left"
    | "down,none,ambiguous,left,right,up"
    | "down,none,ambiguous,left,up,right"
    | "down,none,ambiguous,right,left,up"
    | "down,none,ambiguous,right,up,left"
    | "down,none,ambiguous,up,left,right"
    | "down,none,ambiguous,up,right,left"
    | "down,none,left,ambiguous,right,up"
    | "down,none,left,ambiguous,up,right"
    | "down,none,left,right,ambiguous,up"
    | "down,none,left,right,up,ambiguous"
    | "down,none,left,up,ambiguous,right"
    | "down,none,left,up,right,ambiguous"
    | "down,none,right,ambiguous,left,up"
    | "down,none,right,ambiguous,up,left"
    | "down,none,right,left,ambiguous,up"
    | "down,none,right,left,up,ambiguous"
    | "down,none,right,up,ambiguous,left"
    | "down,none,right,up,left,ambiguous"
    | "down,none,up,ambiguous,left,right"
    | "down,none,up,ambiguous,right,left"
    | "down,none,up,left,ambiguous,right"
    | "down,none,up,left,right,ambiguous"
    | "down,none,up,right,ambiguous,left"
    | "down,none,up,right,left,ambiguous"
    | "down,left,none,right,up"
    | "down,left,none,up,right"
    | "down,left,none,ambiguous,right,up"
    | "down,left,none,ambiguous,up,right"
    | "down,left,none,right,ambiguous,up"
    | "down,left,none,right,up,ambiguous"
    | "down,left,none,up,ambiguous,right"
    | "down,left,none,up,right,ambiguous"
    | "down,left,right,none,up"
    | "down,left,right,none,ambiguous,up"
    | "down,left,right,none,up,ambiguous"
    | "down,left,right,up,none"
    | "down,left,right,up,none,ambiguous"
    | "down,left,right,up,ambiguous,none"
    | "down,left,right,ambiguous,none,up"
    | "down,left,right,ambiguous,up,none"
    | "down,left,up,none,right"
    | "down,left,up,none,ambiguous,right"
    | "down,left,up,none,right,ambiguous"
    | "down,left,up,right,none"
    | "down,left,up,right,none,ambiguous"
    | "down,left,up,right,ambiguous,none"
    | "down,left,up,ambiguous,none,right"
    | "down,left,up,ambiguous,right,none"
    | "down,left,ambiguous,none,right,up"
    | "down,left,ambiguous,none,up,right"
    | "down,left,ambiguous,right,none,up"
    | "down,left,ambiguous,right,up,none"
    | "down,left,ambiguous,up,none,right"
    | "down,left,ambiguous,up,right,none"
    | "down,right,none,left,up"
    | "down,right,none,up,left"
    | "down,right,none,ambiguous,left,up"
    | "down,right,none,ambiguous,up,left"
    | "down,right,none,left,ambiguous,up"
    | "down,right,none,left,up,ambiguous"
    | "down,right,none,up,ambiguous,left"
    | "down,right,none,up,left,ambiguous"
    | "down,right,left,none,up"
    | "down,right,left,none,ambiguous,up"
    | "down,right,left,none,up,ambiguous"
    | "down,right,left,up,none"
    | "down,right,left,up,none,ambiguous"
    | "down,right,left,up,ambiguous,none"
    | "down,right,left,ambiguous,none,up"
    | "down,right,left,ambiguous,up,none"
    | "down,right,up,none,left"
    | "down,right,up,none,ambiguous,left"
    | "down,right,up,none,left,ambiguous"
    | "down,right,up,left,none"
    | "down,right,up,left,none,ambiguous"
    | "down,right,up,left,ambiguous,none"
    | "down,right,up,ambiguous,none,left"
    | "down,right,up,ambiguous,left,none"
    | "down,right,ambiguous,none,left,up"
    | "down,right,ambiguous,none,up,left"
    | "down,right,ambiguous,left,none,up"
    | "down,right,ambiguous,left,up,none"
    | "down,right,ambiguous,up,none,left"
    | "down,right,ambiguous,up,left,none"
    | "down,up,none,left,right"
    | "down,up,none,right,left"
    | "down,up,none,ambiguous,left,right"
    | "down,up,none,ambiguous,right,left"
    | "down,up,none,left,ambiguous,right"
    | "down,up,none,left,right,ambiguous"
    | "down,up,none,right,ambiguous,left"
    | "down,up,none,right,left,ambiguous"
    | "down,up,left,none,right"
    | "down,up,left,none,ambiguous,right"
    | "down,up,left,none,right,ambiguous"
    | "down,up,left,right,none"
    | "down,up,left,right,none,ambiguous"
    | "down,up,left,right,ambiguous,none"
    | "down,up,left,ambiguous,none,right"
    | "down,up,left,ambiguous,right,none"
    | "down,up,right,none,left"
    | "down,up,right,none,ambiguous,left"
    | "down,up,right,none,left,ambiguous"
    | "down,up,right,left,none"
    | "down,up,right,left,none,ambiguous"
    | "down,up,right,left,ambiguous,none"
    | "down,up,right,ambiguous,none,left"
    | "down,up,right,ambiguous,left,none"
    | "down,up,ambiguous,none,left,right"
    | "down,up,ambiguous,none,right,left"
    | "down,up,ambiguous,left,none,right"
    | "down,up,ambiguous,left,right,none"
    | "down,up,ambiguous,right,none,left"
    | "down,up,ambiguous,right,left,none"
    | "down,ambiguous,none,left,right,up"
    | "down,ambiguous,none,left,up,right"
    | "down,ambiguous,none,right,left,up"
    | "down,ambiguous,none,right,up,left"
    | "down,ambiguous,none,up,left,right"
    | "down,ambiguous,none,up,right,left"
    | "down,ambiguous,left,none,right,up"
    | "down,ambiguous,left,none,up,right"
    | "down,ambiguous,left,right,none,up"
    | "down,ambiguous,left,right,up,none"
    | "down,ambiguous,left,up,none,right"
    | "down,ambiguous,left,up,right,none"
    | "down,ambiguous,right,none,left,up"
    | "down,ambiguous,right,none,up,left"
    | "down,ambiguous,right,left,none,up"
    | "down,ambiguous,right,left,up,none"
    | "down,ambiguous,right,up,none,left"
    | "down,ambiguous,right,up,left,none"
    | "down,ambiguous,up,none,left,right"
    | "down,ambiguous,up,none,right,left"
    | "down,ambiguous,up,left,none,right"
    | "down,ambiguous,up,left,right,none"
    | "down,ambiguous,up,right,none,left"
    | "down,ambiguous,up,right,left,none"
    | "ambiguous,none,left,right,up,down"
    | "ambiguous,none,left,right,down,up"
    | "ambiguous,none,left,up,right,down"
    | "ambiguous,none,left,up,down,right"
    | "ambiguous,none,left,down,right,up"
    | "ambiguous,none,left,down,up,right"
    | "ambiguous,none,right,left,up,down"
    | "ambiguous,none,right,left,down,up"
    | "ambiguous,none,right,up,left,down"
    | "ambiguous,none,right,up,down,left"
    | "ambiguous,none,right,down,left,up"
    | "ambiguous,none,right,down,up,left"
    | "ambiguous,none,up,left,right,down"
    | "ambiguous,none,up,left,down,right"
    | "ambiguous,none,up,right,left,down"
    | "ambiguous,none,up,right,down,left"
    | "ambiguous,none,up,down,left,right"
    | "ambiguous,none,up,down,right,left"
    | "ambiguous,none,down,left,right,up"
    | "ambiguous,none,down,left,up,right"
    | "ambiguous,none,down,right,left,up"
    | "ambiguous,none,down,right,up,left"
    | "ambiguous,none,down,up,left,right"
    | "ambiguous,none,down,up,right,left"
    | "ambiguous,left,none,right,up,down"
    | "ambiguous,left,none,right,down,up"
    | "ambiguous,left,none,up,right,down"
    | "ambiguous,left,none,up,down,right"
    | "ambiguous,left,none,down,right,up"
    | "ambiguous,left,none,down,up,right"
    | "ambiguous,left,right,none,up,down"
    | "ambiguous,left,right,none,down,up"
    | "ambiguous,left,right,up,none,down"
    | "ambiguous,left,right,up,down,none"
    | "ambiguous,left,right,down,none,up"
    | "ambiguous,left,right,down,up,none"
    | "ambiguous,left,up,none,right,down"
    | "ambiguous,left,up,none,down,right"
    | "ambiguous,left,up,right,none,down"
    | "ambiguous,left,up,right,down,none"
    | "ambiguous,left,up,down,none,right"
    | "ambiguous,left,up,down,right,none"
    | "ambiguous,left,down,none,right,up"
    | "ambiguous,left,down,none,up,right"
    | "ambiguous,left,down,right,none,up"
    | "ambiguous,left,down,right,up,none"
    | "ambiguous,left,down,up,none,right"
    | "ambiguous,left,down,up,right,none"
    | "ambiguous,right,none,left,up,down"
    | "ambiguous,right,none,left,down,up"
    | "ambiguous,right,none,up,left,down"
    | "ambiguous,right,none,up,down,left"
    | "ambiguous,right,none,down,left,up"
    | "ambiguous,right,none,down,up,left"
    | "ambiguous,right,left,none,up,down"
    | "ambiguous,right,left,none,down,up"
    | "ambiguous,right,left,up,none,down"
    | "ambiguous,right,left,up,down,none"
    | "ambiguous,right,left,down,none,up"
    | "ambiguous,right,left,down,up,none"
    | "ambiguous,right,up,none,left,down"
    | "ambiguous,right,up,none,down,left"
    | "ambiguous,right,up,left,none,down"
    | "ambiguous,right,up,left,down,none"
    | "ambiguous,right,up,down,none,left"
    | "ambiguous,right,up,down,left,none"
    | "ambiguous,right,down,none,left,up"
    | "ambiguous,right,down,none,up,left"
    | "ambiguous,right,down,left,none,up"
    | "ambiguous,right,down,left,up,none"
    | "ambiguous,right,down,up,none,left"
    | "ambiguous,right,down,up,left,none"
    | "ambiguous,up,none,left,right,down"
    | "ambiguous,up,none,left,down,right"
    | "ambiguous,up,none,right,left,down"
    | "ambiguous,up,none,right,down,left"
    | "ambiguous,up,none,down,left,right"
    | "ambiguous,up,none,down,right,left"
    | "ambiguous,up,left,none,right,down"
    | "ambiguous,up,left,none,down,right"
    | "ambiguous,up,left,right,none,down"
    | "ambiguous,up,left,right,down,none"
    | "ambiguous,up,left,down,none,right"
    | "ambiguous,up,left,down,right,none"
    | "ambiguous,up,right,none,left,down"
    | "ambiguous,up,right,none,down,left"
    | "ambiguous,up,right,left,none,down"
    | "ambiguous,up,right,left,down,none"
    | "ambiguous,up,right,down,none,left"
    | "ambiguous,up,right,down,left,none"
    | "ambiguous,up,down,none,left,right"
    | "ambiguous,up,down,none,right,left"
    | "ambiguous,up,down,left,none,right"
    | "ambiguous,up,down,left,right,none"
    | "ambiguous,up,down,right,none,left"
    | "ambiguous,up,down,right,left,none"
    | "ambiguous,down,none,left,right,up"
    | "ambiguous,down,none,left,up,right"
    | "ambiguous,down,none,right,left,up"
    | "ambiguous,down,none,right,up,left"
    | "ambiguous,down,none,up,left,right"
    | "ambiguous,down,none,up,right,left"
    | "ambiguous,down,left,none,right,up"
    | "ambiguous,down,left,none,up,right"
    | "ambiguous,down,left,right,none,up"
    | "ambiguous,down,left,right,up,none"
    | "ambiguous,down,left,up,none,right"
    | "ambiguous,down,left,up,right,none"
    | "ambiguous,down,right,none,left,up"
    | "ambiguous,down,right,none,up,left"
    | "ambiguous,down,right,left,none,up"
    | "ambiguous,down,right,left,up,none"
    | "ambiguous,down,right,up,none,left"
    | "ambiguous,down,right,up,left,none"
    | "ambiguous,down,up,none,left,right"
    | "ambiguous,down,up,none,right,left"
    | "ambiguous,down,up,left,none,right"
    | "ambiguous,down,up,left,right,none"
    | "ambiguous,down,up,right,none,left"
    | "ambiguous,down,up,right,left,none"
    | ScrollDirection[]