%%%%$$%%%%%%%%%%$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$%%$$$$%%%%$%%%%%%%%%%%$$%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%%$&%%%%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%&%%%%%%%%%%%%%%%%%%%%$%$%%%$$%%%&$$$%%%%%%%%%%%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$%%%%%%%%%%%%%%%%%%%$$%%%%%%%%%%%%%%$$%%%%%%%%%%%%%%%%&%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%%%%%%%%%%&$$%%%%%%&%%%%%%%%%%%%%%&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%%%$%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&%%%%%%%%%%%%%%&%%%%%%%%%$%%%%%%%%%%%%%%%%%%$$%%$$$$%%%%%%%%%$%%$%%%%%%%%$%%%%%%%&%%%%%%$%$$$%%%%%%%$%%%&%%%$$$$$$$$%%%%$%%%%%$%%%%%%%%%%$%%%%%%%%%%%%%%%%%$$%%%%%%%%%%%%%%%$$$$$$%%%$%$%%%&%%%%$%%%%%%%%%$%%%%%%%%%%%%%%%$$%%%%%%%%%%%%%%%$$$%%$%%$%%%$$%%%%%$$%%%%%%%%%%%%$%%%%%%%%$$%%%$$%%%%%$$$$%%%%$%$$%%%%%%%%%%%%%%%%%$$$$$$%%%%%$$$%%%%%%$$$$%%%$%%%%%%%%%%%%%%%$$%%%%%%%%%%%%%%&%%%%%$$$$%%%%$$$$$%%%%%%$$$$%%%%%$%%%%%$%%$%%%%%$$%%%%%%%%%%%%%%%%&$%%%%%%%%%%%%$$%%%%%$$%%%$%%%%%%%%%%%%%$%%%%%%%%%%%%%$%%%%%%%%%%$%%%$%%%%%$%%$%$%%&%%%%$$$$%%%%%%%$$%$%%%%%%%$%%%%%%%%%%$%%%%%%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%$%$$%%%%%%%%%%%%%%%%$%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%%%%%$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%$%%%%%$%$%%%%%%$$$%%%%$$$$%%%%%%%%%$%%%%%%%%%$%%%%%%%%%%%%%&%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%$%$%%%%&%%%%%%%%%%%%%%%%%%%$%%$%%%%&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%%%%%%%%%%&%%%%%%%%%%%%%%&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%$$$$%%%%%%%%%%%%%%%%%%&%%%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&%$$$$%%%%%%%%%%%%%%%%%%%%$%%$%%%%%%%%%%%%%%%%%%%%%%%&%%%%%%%%%%%%$$%%%%%%&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&%$%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%&%%%%%%%$%%%%%%%%%%%%%%%$$%%%%%%%%%%%%&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%$%%%%%%%%%%%$%%%%%%%%%%%%%&%%%%%%%%%%%%%%%&%%$$%$%%%%%%%$%%%%$%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%&%%%%%%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$%%%%%%%%&%%%%%%%%$%%%%%%%%%%%%%%$%$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$%%%%%%%%%%%%%%$%$%%%%%%%%%%%%%$%$$%%%%%%%%%%%%%%%%%%%%%%%%%&%%%%%$%%%%%%%&%%%%$$%$%%%%%%%%%%%%$$$$%%%%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&%%%%%%%%%%%%%%&%%%%%%%%%%%%%%%%%%%$$$%%%%%$%$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%%%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%$&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%$%%%%%%%%%%%%%%%%%%%%$%%%%$$%$$%%$%%%%%%%%%%%%$$$$%%%%%%%%%%%%%%%%%%%%$%%$$$$$%%%%$%$$%%%%$$$$$$%%%%%%%%%%$%%%%$$$&%%%%%%%%%%%$$%$%%%%%%$$$$$$%%%%%%$%%%%%%%$$%$%%%%%%%%%%%%%$$$$$%%&%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%$$%%%%%%$%%$$%%%%&%%%%%%$$$%$%%%%%%%%%%%%%%%$%%%%%%%$%%%%$%%%%%%%%%%%%%%%%%$%%$$$$&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$%%%%%%%%%%%$%%%$$$%%%%%%%%%%%%%%%$%%%%%%%$%%%%%%%%$%%%%%%%%%%%$$%%%%%%%%%%$$%%$%$$%%%%%%%%%%%%$$%$%%%%%%%%%%%%%%%%$%$%%%%%%%%%$$$$%%%%%%%%$%%%%$$$%%%%%%%%%%%%$$$$%%%%%%%%%%%%%%%%$$%%%%%%%%$%%%$$$$%%%%$$%%%%%%%%$$$%$%%$%%%%%%%%%%%%%%%$%%%%%%%$%%%%%%%%%%%%%%%%%$%%%$$%%%%%%%%%%%$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%$%%%%%%%%%%$$%$%%%%%%%%%&%%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%$$%$$%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%%%$%%%%%%%$%%%%%%%$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%$$$%%%%%%%%%%%%$$%%%%%%%%$$%%%%%%%%%%%%%%%%%%%%%%%%%$%$%%%%%%%%%%$$%%%%%%%%%%%%$$%%%%%%$$%$%%%%%%%%%%%%%%%%%%%%%%%%$$%%%%%%%%%%$%%$%%%%%&%%%%%%$$%%%%%%$$$$%%%%%%%%%%%%%%%%%%%%%%&%$$%%%%%%%%%$%$$$%%%%%%%%%%%%$%%$%%%%$$$$%%%%%%%%%$$$$$$%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%$$%%%%%%%%%$$$$%%%$%$$%%%%%%%%%%&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%$%%&%%%%%$%$$$%%%%%$%%%%%%%%%&%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%$$$%%%%%%%%%%%%$%%%%%$$%%%%%%%%%%%%%%%%%%%%%%%%&%&%%%%%%%%%%%%%%$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%$%%%%%%%%%%%%$$%%%%%%%%%%$%%%$$$%$$$%%%%%%%%%%%$%%%%%%%%%%%%%%%%%%$%%%%%%%%%%%%$%%&%%%%%$%%%%%$$%$%$%%%%%%%%%%$$%%%%%%%%%%%%%%%%%%%%%%%$%%%%$%$$%%%%%%%%$%%%$%$$$%%%%%%%%%%%$$$$%%%%%%%%%%%%%%%%$%%%%%%%%%%%$$$$%%%%%%%%$$%$