....,,iiiittiiiiiiiiiittii;;..                                      
                                                                                                                              ..;;;;iijjffGGGGGGLLjjiiiijjLLLLLLjjii..                                  
                                                                                                                        ..::iijjLLLLLLGGGGLLffjjLLLLffjjiiiittttjjLLtt::..                              
                                                                                                                        ;;jjGGLLjjLLLLGGGGGGLLLLLLLLLLjjtt;;,,,,ii;;iiiiii..                            
                                                                                                                      ::jjGGLLttjjLLGGGGLLffLLLLffffLLLLLLLLjjiiiiiiiiiiii;;..                          
                                                                                                                    ::jjGGGGttttLLGGGGGGGGGGLLjjjjjjttttttttttttttttjjffjjjjtt::                        
                                                                                                                  ..iiGGGGjjttLLLLLLGGLLLLLLffjjttii,,,,::,,,,,,,,,,iiffGGDDEEGG::                      
                                                                                                                  ;;LLGGjjttLLLLffLLLLffLLLLLLffttii;;;;iittttttii;;,,,,,,iijjGGLL::                    
                                                                                                              ..,,iittiittjjjjjjLLLLLLffjjjjiittjjffLLLLffjjttttttttiiii;;;;,,;;LLff,,                  
                                                                                                      ..;;,,;;ii;;iiiittiittttjjjjjjttii,,;;iiiiiittjjLLGGDDGGLLLLjjttttjjttjjGGGGEEjj::                
                                                                                                    ..iiLLGGLLLLLLffii,,iittttttttttii,,;;,,,,,,;;iiiittjjjjjjffLLLLLLLLLLLLGGDDEEKKEEjj,,..            
                                                                                                  ..iiLLDDDDDDGGffii;;ttffjjjjLLjjttiitttttttt;;;;iittjjjjjjffLLLLLLjjLLLLLLGGEEEEKKEEEEfftt::          
                                                                                                ::;;jjEEEEEEGGLLLLttjjLLGGGGGGiijjLLffLLffttii;;,,;;ttjjjjttttttii;;iittLLGGDDDDEEEEEEEEGGfftt::        
                                                                                              ::ttttDDEEDDGGLLGGjjjjLLGGGGDDDDGGttttffjjtttt;;,,;;tttttt;;;;;;iiiiiiiijjLLGGGGEEGGDDKKEEGGLLjjtt        
                                                                                            ::iittGGDDGGGGGGDDGGiiffGGGGGGLLLLLLLLLLjjtttt;;,,iiiiii;;;;iittttii;;;;;;iijjffGGDDDDGGEEKKGGffLLff::      
                                                                                        ::;;ttjjGGGGGGDDDDDDDDjjjjLLLLGGLLjjjjttjjLLffjjiittjjttttttjjjjjjttii;;;;,,;;iittLLGGDDEEDDEEEEGGttjjGGtt..    
                                                                                    ::;;ttttLLGGGGGGGGGGGGGGffttLLLLGGffttffffjjjjttttttjjjjjjjjttjjttiiiiii;;;;,,,,;;ttttffLLDDEEEEEEDDjjiijjGGff..    
                                                                                ::;;ttffLLGGLLLLLLLLLLjjjjffttjjLLGGffjjjjLLjjjjjjttjjffffjjttiiii;;,,iiii;;,,,,,,iiiittjjLLGGGGEEEEDDffff;;ttGGLL::    
                                                                            ..;;iiffGGGGLLLLGGDDGGLLLLLLttjjttLLffjjjjLLDDLLttjjjjjjffffttii;;;;,,;;ttttii;;;;;;;;;;iittjjjjLLGGGGGGLL;;LLii;;GGLL::    
                                                                          ..;;jjDDEEDDGGGGEEEEGGGGGGDDGGLLttttLLLLLLGGGGLLjjttjjjjffjjii;;;;;;iittttiiiiii;;ii;;;;ttttiittttjjLLGGjjjj,,ttjj;;LLLLii..  
                                                                        ..;;LLEEEEGGLLGGDDDDGGGGDDDDDDLLLLttjjLLLLGGLLjjjjttjjffGGLLttttjjttjjjjttttttttiiii;;;;ttttiiiittiittjjttjjjj,,,,jjttjjLLtt..  
                                                                        ;;GGKKEEGGLLffLLGGGGLLLLLLGGLLLLLLttLLjjjjjjttjjjjjjffLLLLLLffLLGGGGGGffffjjttiiiiiittjjii;;iittiiiiiiiiiijjtt;;..iittjjfftt    
                                                                      ;;GGKKKKGGjjGGEELLjjjjffjjjjttjjjjjjiijjjjjjjjLLLLjjjjjjffjjjjjjjjffGGGGffjjttttttttttttiiiittii;;;;ii;;,,;;ttjj;;::;;ttjjfftt    
                                                                ....ttLLGGGGLLLLGGEEEEEELLiittjjttttttffiittjjffffjjttjjjjttttjjjjjjjjjjjjjjLLGGLLjjjjttttttttttttii;;,,;;,,,,,,;;;;ttii::;;iijjfftt..  
                                                              ::jjDDGGGGDDDDDDEEEEEEEEDDEEDDffttiittttttjjffjjtt;;,,ttjjii;;iijjLLGGGGLLjjttffGGGGLLffjjjjjjttii;;;;;;,,,,;;,,,,,,iiiiii::iittttLLjj::  
                                                            ttjjffjjiiGGKKEEEEDDEEEEGGGGDDEEDDGGDDGGLLjjffjjttttjjffjjii;;,,,,iiGGEEEEEELLjjjjLLDDLLii,,,,,,,,iittttii,,,,;;,,,,,,;;ttjj,,iijjttfftt    
                                                        ..ttttttjjiiffEEEEEEDDDDEEGGGGEEDDEEGGGGDDLLLLLLLLLLLLGGGGjjii;;,,,,,,,,iijjGGKKDDGGjjttLLLLii;;;;iittjjtt;;,,::,,;;,,,,,,iijjtt,,iiffttLLtt    
                                          ..::..    ::;;ttttjjjjjjLLGGDDGGGGGGLLLLGGEEDDDDDDGGGGLLGGLLLLGGGGGGGGjjii;;;;,,,,::,,,,;;jjEEEEGGLLiittffjjiitttt;;,,::::::::,,,,,,,,;;ttjjtt,,;;LLttLLLL::  
                                        ::ffffjj;;ttjjttiijjLLGGGGGGLLLLLLLLLLGGDDEEEEGGGGGGGGLLGGGGLLGGDDGGGGjjiiii;;;;,,,,::::,,,,;;jjii;;LLjjttjjjj;;;;,,,,::::::::::,,,,,,,,;;jjffttiiiiffjjjjGG..  
                                        ttGGGGGGGGGGGGGGGGGGGGGGLLLLGGGGDDDDDDEEDDEEGGffLLGGGGGGLLLLffGGGGLLffttiiii;;,,,,::......::,,;;;;iiffjjttttii,,,,,,::::::::::::::,,,,,,iijjffttttiiffjjjjGG::  
                                      ::GGDDEEKKKKEEDDDDGGGGDDDDGGGGEEEEEEEEEEEEEEGGjjLLLLGGLLGGffffffGGGGffjjttii;;;;,,,,::........::,,,,,,iittttii;;,,,,::::::::::::::::,,;;;;jjffffjjjjiiLLjjffff;;  
                                      ttGGDDKKKKKKKKEEEEEEEEEEDDGGEEKKEEGGLLLLffjjjjjjLLGGGGjjLLffjjjjGGLLjjttttii;;;;,,,,::............::,,::,,ii;;,,::::::::::::::::::::,,;;;;jjLLLLjjffttffjjLLLLtt  
                                    ;;LLDDKKKKKKEEEEEEEEEEEEEEDDDDDDGGGGLLGGGGGGLLjjLLGGDDffttffffjjjjGGjjjjttttii;;;;,,,,::..............::::,,;;,,::..::::,,,,,,::::::::,,,,ttjjLLLLffLLjjttjjLLLLtt  
                                  ..ttGGEEDDGGGGDDEEEEEEEEEEDDGGGGGGEEEEEEEEEELLttGGGGLLLLii;;jjjjttLLLLjjttttiiii;;;;,,,,::..............::::,,,,::....::,,,,;;ii,,::::,,,,;;ttLLLLLLffLLjjttttLLffii  
                              ::,,;;jjGGjjjjGGLLLLLLGGDDffffGGGGDDEEEEDDDDEELLjjDDGGjjjjjj;;;;ttttLLGGffttttttiiiiii;;,,,,,,::..........::::,,,,,,....::,,;;iittffLLjjii,,,,;;ttjjLLLLffLLLLttttjjff;;  
                            ..;;ttjjGGLLGGEEEEDDGGGGGGDDGGDDDDDDDDDDDDEEDDGGffDDGGffLLffjjii;;ttffGGGGjjttiiiiiiiiii;;;;,,,,,,,,,,,,,,,,::,,,,,,::..::,,;;jjLLLLjjjjGGGGjjiiiiLLjjjjLLLLjjLLttiittjj::  
                        ..;;ttjjLLGGGGLLffjjjjjjffLLffffGGGGLLLLGGDDDDDDDDLLGGLLffLLLLGGjjiijjGGGGDDLLjjttii;;;;iiii;;;;;;;;;;;;;;;;,,,,,,,,,,::....::,,;;ttEEEEGGttiijjGGffjjEEGGiiLLLLffLLjjiiiiii..  
                      ..iiii;;iittffttii;;;;;;;;,,;;iittttjjjjffGGGGGGGGGGGGLLLLGGLLLLttiiLLGGLLGGEEGGjjii;;;;;;;;iiiiii;;;;,,,,,,ii,,,,,,,,,,::..::,,::::,,GGEEEEGGii,,iiffDDEEDDffLLLLffLLiittiiii..  
              ..;;iiiiii;;,,ttjjjjttttttii;;,,,,,,,,,,;;;;iiiittLLLLLLGGLLLLffLLjjiiiijjGGGGLLLLEEKKGGjjii;;,,,,,,;;ii;;,,,,,,::;;jj,,,,,,,,::..::,,::::::,,iiLL;;LLGGii;;jjKKEEDDGGGGffffLLiijjiitt..  
                  ....;;ttjjLLjjjjttiiiiiiii;;,,,,,,,,,,,,;;;;iiffffLLLLffttttjjjjGGGGDDEEGGGGGGEEKKGGjjii;;,,,,,,::LLff;;,,::,,;;fftt;;,,,,::..::,,::..::,,;;ii;;GGEEjjttEEKKKKDDLLffLLffttttttiiii..  
                  ..ttGGLLjjttiiii;;;;;;,,,,;;;;,,::::::,,,,;;iijjjjffffjjjjGGEEGGGGDDEEDDGGDDEEEEKKGGjjii;;,,,,::..ttGGjj;;::::,,ttGGffii,,....,,,,::::..::,,;;jjGGGGLLEEKKKKKKDDffffffjjiittiijjjj,,  
                ..jjffjjttttiiii;;;;;;,,,,,,,,,,;;,,::::,,,,,,iijjffGGffffjjGGEEGGLLEEDDLLGGEEDDEEEEDDjjii;;,,,,::::,,jjttjjii,,::,,jjLLtt,,,,::,,,,::::::::,,,,;;iittEEKKKKKKKKDDLLffLLttttttiittjjii  
                ;;jjjjjjttiiiiii;;;;,,,,,,,,::,,,,;;,,::,,,,,,iijjGGGGjjLLjjGGEELLLLDDGGLLGGDDDDEEEEDDfftt;;,,,,::::;;ii;;;;ttjj,,,,iiffjjii;;;;,,,,::::::::::,,;;;;DDKKEEKKKKEEGGGGLLjjttttiittiijjii  
              ::jjjjjjjjttiiii;;;;,,,,,,,,::::::::,,;;,,::,,;;ttffGGGGjjLLttLLKKLLLLGGLLLLDDGGGGEEDDDDLLtt;;,,,,::,,iiiiii::::ttjj;;;;iijjjjjjii,,;;,,::::::,,,,,,LLKKKKEEKKEEDDGGGGDDffttttttjjiiff;;  
            ..jjLLjjjjttttiiii;;;;,,,,::::::::::::,,;;;;,,,,;;iiLLGGLLLLGGttjjEEjjffGGffGGGGGGDDGGGGGGGGtt;;,,,,::,,;;ii;;ii::  iijjii;;;;ii;;,,,,;;,,,,::,,,,,,jjKKKKKKEEEEEEGGDDDDGGLLffttttii;;jj::  
            ttffffjjjjttttiiii;;,,,,,,,,::::::..::,,,,;;;;,,;;ttLLGGjjLLGGjjttDDffjjLLjjGGGGGGGGGGGGGGGGjj;;,,::,,,,;;ttii,,ii....;;jjtt;;,,,,,,,,;;,,,,,,,,,,iiEEKKKKEEDDEEEEEEEEGGGGGGjjiitt,,;;ii..  
          ,,ffLLffjjjjttiiii;;;;,,,,,,::::......::,,,,;;ii,,;;jjGGLLiiGGDDLLttGGjjttjjLLGGLLGGGGGGGGGGGGff;;,,::,,,,;;iitt;;,,ii,,..,,ttjj;;,,;;;;;;,,,,,,,,,,GGKKKKKKEEEEEEEEEEGGLLGGLLjjiittii;;,,    
          jjLLffffjjjjttiiii;;;;,,,,::::........::::,,,,;;;;;;jjffttjjEEEEGGttGGttttLLGGLLGGGGGGLLGGGGGGLLii,,::::,,,,;;ttii;;;;iiii;;jjDDGGttttii;;;;,,,,,,ffKKEEEEKKEEEEEEEEEEGGLLffttjjttiittii..    
        ,,LLLLLLffjjjjttii;;;;,,,,,,::::..........::,,,,;;ii;;tt;;ttLLEEEELLttLLjjttLLLLLLGGGGLLLLLLGGLLLLtt,,,,::::::,,iiiittii;;iijjjjttttjjiiii;;;;;;,,ffKKKKEEEEKKEEEEDDEEDDLLLLffjjtttttttt;;      
        ttLLLLffffffjjttiiii;;;;,,,,::..........::::,,,,;;ii;;,,jjffLLEEDDLLjjLLjjttLLLLLLLLLLLLLLLLLLLLLLjj;;,,,,....::,,;;iiiiiiiiii;;,,,,,,;;iiii;;iiGGKKKKKKEEKKEEEEEEGGDDGGLLLLLLjjttjjjjii,,      
      ..ffLLLLffffffjjttiiii;;,,,,,,::..........::::,,,,iiiittjjGGjjffDDLLLLLLttttjjGGLLLLLLLLLLLLLLLLLLfffftt;;,,::....::,,,,;;;;;;,,,,,,,,,,,,;;iiLLEEKKKKKKEEEEEEKKEEEEDDLLGGjjffLLLLffjjttii..      
      ,,GGLLLLffffjjjjttiiii;;;;,,,,::::........::,,,,;;iittttjjGGffjjLLLLffttiittLLGGLLLLLLffLLLLLLLLLLffjjjjii;;,,,,::::::,,,,,,,,::,,,,,,,,iiffEEKKKKKKKKKKKKEEEEEEDDEEDDiiLLiijjLLjjttttiiii..      
      ;;LLLLffffjjjjjjttttii;;;;,,,,::::::....::::,,;;iiiittttjjGGLLjjLLjjttjjjjjjGGGGGGLLLLLLLLLLLLLLLLffffjjjj;;;;,,,,::,,,,::::,,,,;;iijjGGEEKKKKKKKKKKKKKKEEEEEEEEDDKKDD;;jjtt,,ffjjiijjii;;        
      iiLLLLffffjjjjjjttttttii;;,,,,,,,,::::::::::,,iiiiiijjttjjLLffLLffffLLjjjjGGLLLLGGGGLLLLLLLLLLLLLLLLffLLLLLLii;;,,,,,,::,,iiffGGEEKKKKKKKKKKKKKKKKKKKKEEDDDDEEGGEEKKEEiittjj,,jjff;;tt;;;;        
      jjLLLLffffffjjjjjjttiiii;;;;;;,,,,,,::::,,,,,,;;;;ttjjttjjLLLLffjjLLjjLLGGLLLLLLGGGGLLLLLLLLLLLLLLLLLLffGGEEDDjjiiiiiijjDDEEKKKKKKKKEEKKKKKKKKKKKKKKEEEEGGGGLLGGKKKKDDttiiff;;iijjii;;;;,,        
    ..ffLLLLffjjjjjjjjttttttii;;;;;;,,,,,,,,,,,,,,,,,,;;ttjjttjjLLLLffffLLDDGGGGLLffLLGGGGGGLLGGGGGGGGLLLLffLLEEEEEEEEEEKKKKKKKKEEEEKKKKKKKKKKKKKKKKKKKKEEEEEEEELLjjEEKKEEGGttiiLLii;;jj;;;;ii..        
    ::LLLLLLffjjjjjjjjttttttiiii;;;;;;;;,,,,,,,,,,,,;;;;jjffttttjjLLffLLGGGGGGGGffffLLLLGGGGGGGGGGGGLLLLffffDDEEEEEEEEKKKKKKKKKKEEEEKKKKKKKKKKKKKKKKKKEEEEEEEEGGjjGGEEEEEEGGttiiLLii;;tt;;,,::..        
    ::LLLLLLffjjjjjjjjttttiiiiiiii;;;;;;;;,,,,,,,,;;;;;;ffffttiijjffjjLLGGLLLLffjjffLLLLGGGGLLLLLLffLLjjffGGDDEEEEEEEEEEEEKKEEEEEEKKKKKKKKEEKKKKKKKKEEDDEEEEGGffGGEEEEEEGGLL;;ttff,,;;ii;;;;            
    ,,GGLLLLffffjjjjjjjjttiiiiiiii;;;;;;;;;;;;;;;;;;;;iijjffiiiijjjjLLLLGGGGffttjjLLLLGGLLLLLLffffffjjjjGGGGDDEEEEEEEEEEEEKKKKEEKKKKKKKKKKEEKKKKKKKKEEDDEEDDGGGGEEEEEEGGGGttiijjii,,iiii,,,,            
    ;;GGLLLLffffjjjjjjttttiiiiiiii;;;;;;;;;;;;;;;;;;;;iijjffiiiiiijjLLLLLLjjttttffffLLLLLLLLLLffffjjjjLLGGGGGGEEEEEEEEEEEEKKKKKKKKKKKKKKEEKKKKKKKKEEGGEEEEGGGGEEEEEEDDDDLLiijjtt,,ttff;;ii,,            
    ttGGLLLLffjjjjjjjjttttttiiiiiiii;;;;;;;;;;;;;;;;;;iijjjjiiiittjjffjjttttttjjffffLLLLffjjffjjjjjjLLLLLLGGGGDDEEEEEEKKEEEEKKKKKKEEEEEEKKKKEEEEKKGGDDEEDDDDEEEEEEGGDDDDjjjjjjiittLLjjiiii::            
    jjLLLLLLffffjjjjjjttttiiiiiiiiii;;;;;;;;;;;;;;;;iiiijjfftttt;;iiiittjjffjjffjjffLLLLffjjjjttttffffffLLLLGGDDEEEEEEEEEEKKEEEEEEEEEEEEEEEEKKEELLGGEEDDEEEEEEEEGGLLGGLLLLLLjjjjLLGGii;;tt,,            
  ::ffLLLLffffjjjjjjjjttttiittiiiiii;;;;;;;;;;;;;;;;iittffLLjjttjjffLLLLLLffffjjjjffffffjjjjttjjjjjjjjjjffLLGGDDEEEEEEEEKKEEEEEEKKKKEEKKKKEEDDLLGGEEEEEEDDEEEEEEGGGGGGLLGGjjLLGGGGLLtt;;tt..            
  ::LLGGLLLLLLffjjjjjjttttttiiiiiiii;;;;;;;;;;;;;;;;iittffjjiittffLLLLLLffjjjjjjjjffffjjjjttiijjjjjjttjjjjjjLLGGEEEEEEEEKKEEEEEEKKKKKKKKDDLLGGEEKKEEEEEEDDEEDDEEDDGGDDGGffGGGGGGffLLttiitt              
  ..LLLLLLLLffffjjjjjjttttttiiiiiiii;;;;;;;;;;;;;;iiiiiijjiiiittjjjjLLjjjjttttjjjjffffjjjjttiiiittttttttttjjffGGEEEEEEEEEEDDEEEEEEKKKKEEEEKKKKEEEEEEEEEEGGEEGGGGGGGGGGLLGGGGGGLLffffttiiii              
  ..LLLLLLLLLLffjjjjjjttttiiiiiiiiii;;;;;;;;;;;;;;iiiiiittiiiittjjLLffttttttjjjjjjffjjjjjjttffttttttttttttttjjGGDDEEEEGGLLEEEEDDEEKKKKKKKKKKKKKKEEEEEEDDGGDDGGGGLLLLffLLGGGGLLLLjjjjtt;;ii              
  ..LLLLLLLLLLffffjjjjttttiiiiiiiiiiii;;;;;;ii;;iiiiiittttiiiittttjjttttttttttjjjjjjjjjjjjttttiittttiiiittttjjLLGGEEDDLLGGKKGGDDKKKKKKKKKKKKEEKKKKEEEEDDGGDDDDLLffffffLLGGLLLLjjiittii;;ii..            
  ..LLLLLLLLffLLjjjjjjttttttiiiiiiiiii;;ii;;;;iiiiiijjjjttiiiiiiiiiiiittttttttttjjjjjjjjjjttiittiittiiiittttjjGGDDDDLLDDKKGGLLEEKKKKKKKKKKKKEEEEEEEEEEDDGGGGDDLLjjttffDDGGffffjj;;;;;;;;;;::            
  ..LLLLLLffffffffjjjjjjttiittiiiiiiiiiiiiiiiiiiiijjLLjjttiiii;;;;iiiiiiiittttttttttjjjjjjttiittiiiiiittttttjjGGDDGGGGDDLLffDDEEGGLLLLGGGGGGLLGGGGDDDDEEGGGGGGLLffttttGGLLjjttffjjtt;;ii::              
  ..LLGGLLLLffjjffjjjjjjttttttiiiiiiiiiiiiiiiiiijjLLGGjjii;;;;;;;;;;iiiiiiiiiittttjjjjjjjjttttttttttttttttjjGGDDGGffjjjjLLGGGGGGLLjjjjjjjjLLLLGGDDDDDDDDGGGGGGttjjffjjjjjjjj;;ffjjff;;ii;;              
  ..LLGGLLLLffffjjjjjjttttiittttttiiiiiiiiiiiittjjLLffttii;;;;;;;;;;;;;;iiiiiiiittjjjjjjjjjjttttiittttjjffLLGGLLLLLLLLGGDDLLjjffffjjjjttjjLLjjLLDDDDGGGGLLGGjj;;jjLLGGGGttjjttLLjjLL;;;;ii::            
    jjGGLLLLffjjjjjjjjttttttttttiiiiiiiiiiiittffffGGjjiiii;;;;;;;;;;;;;;iiiiiiiittjjffffjjjjjjttttttjjLLLLLLGGGGGGGGGGGGffjjjjjjjjttttttjjLLttjjLLGGLLLLGGLL;;ttGGLLLLffttttffLLjjLL,,ii;;;;::          
    jjGGLLLLffjjjjjjjjjjttttiittttiiiiiiiittjjLLLLLLjjii;;;;,,,,;;;;;;;;;;iiiiiittffLLLLffjjjjjjjjjjffGGGGLLGGDDGGLLffjjttttttttttttttttffLLttttffLLLLLLLLiiiiLLLLffLLjjjjffLLjjjjjjii;;,,,,,,..        
    ttGGLLLLffjjjjttttttttttttiittiiiiiittttffGGGGjjiiii;;;;;;,,,,;;;;;;;;;;iiiittLLGGLLLLffffjjffffLLGGLLGGEEDDLLLLLLttttttttttttttttttjjGGLLffffGGLLffttttjjLLffffffffffjjjjjjfftt,,,,,,,,,,,,        
    ttGGGGLLLLjjttttttiittttttttiiiiiittiittffGGLLjjiiii;;;;;;,,,,,,;;;;;;;;iiiittLLDDGGGGLLLLffLLLLGGGGGGDDDDGGGGLLjjttttttiiiiiiiittjjffffLLLLGGGGLLjjjjttjjffLLffLLGGLLjjttjjtt;;,,,,,,,,,,,,        
    ,,GGGGLLffjjttttiittttttttiiiiiittiiiittLLjjjjjjiiii;;;;;;,,,,,,,,,,;;;;;;iiiiGGEEDDGGGGLLLLGGDDGGLLGGGGGGGGGGffjjttttiiiiiiiiiiiiiittffjjffLLffjjttttjjjjLLLLffGGLLjjttjjttii,,,,,,,,,,,,,,,,      
    ::GGGGLLLLjjjjttiittiiiiiiiiiiiiiiiiiijjLLjjttjjjjtt;;;;;;;;,,,,,,;;;;;;;;iiiiGGEEDDDDGGGGGGDDGGjjGGGGLLLLLLffjjttttiiiiiiiiiiiiiiiiiittffffjjttttttttttjjffGGjjttjjjjttiiii;;,,,,,,,,,,,,,,,,..    
    ::GGGGLLffjjttttiittiiiiiiiiiiiiiiiiiijjffjjttiijjjjii;;;;;;,,;;,,;;;;;;;;iiiiDDKKEEDDDDEEDDjjjjLLGGGGLLLLLLjjjjjjiiiiiiiiiiiiiiii;;iittjjttiiiiiiiiiittttjjLLjjiiiittiitt;;,,,,,,,,,,,,,,,,,,,,    
    ..LLGGLLLLjjjjttiittiiiiiiii;;iiiiii;;jjjjjjttttiittjjii;;;;;;;;;;;;;;;;;;iittDDKKKKKKKKLLiittffGGGGGGLLfffffffftt;;;;iiiiiiiiiiii;;;;ttiiiiiiii;;;;;;iiiittjjttiiiijjttii;;;;,,,,,,,,,,,,,,,,,,::  
      jjGGGGLLjjjjttiittiiiiiiiiii;;;;;;iijjttttttttttttiittiiii;;;;;;;;;;;;;;iittKKKKKKEEjjiittffDDGGGGGGLLLLffffffii;;;;iiiiiiiiii;;;;;;,,;;ii;;,,,,;;,,;;;;iiii;;iiiittjjii;;,,,,,,,,,,::::,,,,,,,,  
      ttGGGGffjjttttiiiiiiiiii;;;;;;;;;;iiffttttttttttttttttttiiii;;;;;;;;;;iiiiLLKKDDttiiiijjffDDDDLLGGLLLLffffffffii,,;;iiiiiiiiiiii;;,,,,;;;;,,,,,,,,,,,,,,,,;;;;;;ii;;ttii;;;;,,,,,,,,::::::,,,,,,::
      ;;GGGGffffjjttiiiiiiiiii;;;;;;;;;;ttffttttttjjttttttttttiiiiii;;iiiiiittttttiiiiiittjjGGEEEEGGffGGLLLLfffffffftt,,;;iiiiiiiiiiiiii,,,,;;,,;;,,,,,,,,,,,,,,,,,,,,,,;;iiiiii;;,,,,,,,,::::::,,,,,,,,
      ,,GGGGLLffjjttiiiiiiiiii;;;;;;;;;;ttffttttttttjjttiiiittttttiiiiiiiiiiiiiiiittttttffEEKKEEEEGGffGGLLLLffffffLLtt,,;;iiiiiiiiii;;tt;;,,,,;;;;ii,,,,,,,,,,,,,,,,,,,,,,,,iiii;;,,,,,,,,::::::,,::,,,,
      ;;GGGGffffjjttiiiiiiiiii;;;;;;;;;;ttjjffttiittjjttttiittttttttttttttttttttttttjjGGKKEEEEEEDDGGffGGLLLLffffLLffii;;iiiiiiiiii;;;;ttii,,;;;;,,ii;;,,,,,,,,,,,,,,,,,,,,,,;;tt;;,,,,,,,,::::::::::,,,,
      ,,GGGGLLffjjttiiiiiiiiii;;;;;;;;iijjttjjjjiiiittttttiiiittttttttttttttttttttLLEEKKKKEEEEDDDDLLffGGLLLLLLffffLLii;;iiiittiiii;;;;tttt,,,,;;;;;;tt,,,,,,,,,,,,,,,,,,,,,,,,;;tt;;,,,,,,,,::::::,,,,,,
      ,,GGLLLLLLjjttiiiiiiiiii;;;;;;;;ttLLttttttjjiittttttttttttttttttttttttttffGGKKEEKKKKEEEEDDDDGGffGGGGLLLLffLLffiiiiiiiittiiiiii;;ttjj,,,,;;;;;;ttii,,,,,,,,,,,,,,,,,,,,,,,,iiii;;,,,,,,,,::::,,,,,,
      ,,GGGGLLLLjjttiiiiiiiiii;;;;;;;;jjGGjjjjttjjttttttttttttttttttttttttjjGGDDEEDDDDKKEEEEDDDDDDGGffGGLLLLLLLLLLLLttiiiiiittiiiittttttffii,,,,;;;;ttii,,,,,,,,,,,,,,;;,,,,,,,,,,iiii;;,,,,,,,,::,,::,,
      ;;GGLLLLjjjjttttiiiiiiii;;;;;;;;ffGGffjjjjttjjttttttttttttttttttttffLLGGGGEEGGDDEEKKDDDDDDDDGGffGGGGLLLLLLLLffttiiiiiittiiiiiittjjfftt,,,,,,;;tttt,,,,,,,,,,,,,,,,,,,,,,,,,,,,iiii,,,,,,,,,,::,,::
      ,,GGGGLLffjjttttiiiiiiiiiiiiiiiiGGDDGGffffjjjjjjttttttttttjjjjLLLLLLLLLLffffGGDDEEEEEEDDDDDDGGffGGGGLLLLLLGGLLffttiittiiii;;iittjjfftt,,,,,,;;ttjj;;,,,,,,,,,,,,,,,,,,,,,,,,,,,,ii;;;;,,,,,,,,::::
      ;;GGGGLLffjjttiittiiiiiiiiii;;ttDDDDGGEELLLLLLffffLLffffffGGLLLLffffffffjjjjffEEDDEEDDDDDDDDGGffGGGGLLLLLLGGGGffttttiiii;;;;iittjjffjj,,,,,,;;ttjjii,,,,,,,,,,,,,,,,;;,,,,,,,,,,;;ii;;;;,,,,,,::::
      ttGGLLLLffjjttttiiiiiiiiii;;;;jjGGDDGGDDGGDDDDDDGGffLLffGGLLLLffjjjjffffjjffffGGEEEEDDGGGGDDGGffGGGGGGLLLLLLGGffjjttttttiiiiiittjjffff;;;;;;;;ttjjtt,,,,,,,,,,,,,,,,,,;;,,,,,,,,,,;;ii;;;;,,,,,,::
      ttGGLLLLjjjjttiittiiiiiiiiiiiiGGGGGGGGGGLLDDGGLLLLffLLGGffjjjjjjjjjjffffffjjffGGDDGGDDGGGGGGGGLLLLGGGGGGGGGGGGLLjjttttjjffjjiittjjGGff;;,,;;;;ttjjtt,,,,,,,,,,,,,,,,,,,,;;;;,,,,,,,,iitt;;,,,,,,,,
    ::LLLLLLjjjjttttiiiiii;;iiii;;ttGGDDDDGGDDLLffLLffffffffffjjjjjjjjjjffffjjjjffGGGGffLLDDGGGGGGGGLLLLGGGGGGGGGGGGLLffttttttffGGffttffGGff;;,,;;;;ttjjjj;;,,,,,,,,,,,,,,,,,,,,;;;;,,,,,,,,jjii;;,,,,,,
    ttLLLLjjjjttttiittiiiiiiiiiiiijjGGDDDDGGGGGGLLLLjjffjjjjjjjjjjjjjjjjjjjjjjffGGGGffffLLDDGGGGGGGGGGLLGGGGGGGGGGGGLLffttttttjjGGGGffffGGff;;;;,,;;iijjffii,,,,,,,,,,,,,,,,,,,,,,;;;;,,,,,,iijjii;;;;,,
    ffLLjjjjttttiittttiiiiiiiiiiiiLLDDGGLLffjjjjffGGjjjjjjjjjjjjjjjjjjjjjjjjffGGDDffjjffffGGGGGGGGGGGGLLGGGGGGGGGGGGGGffttttttttffDDDDLLGGff;;;;;;;;iijjffii,,,,,,,,,,,,,,,,,,,,,,,,;;;;,,,,,,jjjjii;;;;
  ;;LLLLjjttttiiiiiiiiiittiiiiiiiiffffjjjjjjjjjjjjffffjjjjjjjjjjjjjjjjjjjjffGGffffjjffffffGGGGGGGGGGGGLLGGGGGGGGGGGGGGGGffttttttffGGEEGGGGffii;;;;;;ttjjfftt,,,,,,,,,,,,,,,,,,,,,,,,;;;;;;,,,,;;fftt;;;;
  ttLLjjttiiiiiiiiiiiiiiiiiittiittjjjjffjjjjjjjjjjjjffffjjjjjjjjjjjjjjjjffLLjjjjjjffjjjjffGGDDGGGGGGGGGGGGGGGGGGGGGGGGGGGGffjjjjffLLGGEEGGffii;;;;;;iijjffjj;;,,,,,,,,,,,,,,,,,,,,,,,,,,;;ii,,,,ttjjii;;
..jjLLjjttiiiiiiii;;iiiittiiiiiittffjjjjjjjjjjjjjjjjffffjjjjjjjjjjjjffffffttjjjjjjjjjjjjffLLDDGGGGGGGGGGGGGGGGGGGGGGGGDDDDGGGGGGjjiittEEEEffii;;;;iiiittffff;;,,,,,,,,,,,,,,,,,,,,,,,,,,,,iiii,,,,fftt;;
::LLLLttiiii;;ii;;;;;;iiiiii;;iijjffjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjffjjttttjjjjjjjjjjjjjjjjffDDDDGGGGGGGGGGGGGGGGGGGGGGDDDDDDLLttiiiittGGDDjjiiii;;;;iittffffii,,,,,,;;,,,,,,,,,,,,,,,,,,,,,,;;ii,,iijjii
iiLLLLttiiii;;;;;;;;;;ii;;;;;;iiffffffffjjjjjjjjjjjjjjjjttjjjjjjjjttttjjjjjjjjjjjjjjjjffjjffGGDDDDGGGGDDGGGGGGGGGGDDDDDDGGjjiiiiiiiiiiLLGGjjii;;iiiiiittffLLtt,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,;;ii,,jjtt
jjLLLLjjiiii;;;;;;;;;;;;;;;;;;jjffffjjjjjjjjjjjjjjjjttjjffffjjjjttttjjffjjjjjjjjjjffffffffGGDDGGDDGGGGGGGGGGGGDDDDDDGGffiiiiiiiittiiiijjLLttiiiiiiiiiittjjGGjj;;,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,;;iiiijj
ffLLffjjiiiiii;;;;;;;;;;;;;;iiffffffffffffjjjjjjjjjjjjffjjjjjjjjjjffjjttjjjjffffffffffffffGGDDDDDDDDGGGGDDDDDDDDGGffttiiiittttiiiiiiiiiiffttiiiiiiiiiittjjLLffii,,,,;;;;,,,,,,,,,,,,,,,,,,,,,,,,,,iiiitt
LLLLffjjiiiiii;;;;;;;;;;;;;;iiffffffffjjjjjjjjjjjjffjjjjjjttjjjjjjttttttttttttttttjjjjffffffGGEEDDEEDDDDDDDDGGffjjttttttttttttttiiiiiiiittttiiiiiiiiiittjjLLGGii;;,,,,;;;;,,,,,,,,,,,,,,,,,,,,,,,,,,iiii
GGLLffjjttiiii;;;;;;;;;;;;;;ttffjjjjjjffjjjjjjjjjjjjjjjjttjjjjttttiittttttttttttjjjjjjffffffLLDDDDDDGGGGLLffjjttttttttttttttttttiiiiiiiiiittttiiiiiiiittjjffGGjj;;,,;;;;,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,ii
LLLLffjjttiiiiii;;;;;;;;;;iittjjjjjjjjjjjjjjjjjjjjjjttttjjttttttttttttttttttttjjjjjjjjjjffffLLLLLLffffjjjjjjttjjjjttttttttttttttttttiiiiiittttttiiiiiittttffGGff;;;;;;;;;;,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
LLffffjjttiiiiii;;;;;;;;;;;;jjjjjjjjjjjjffjjffjjttttttjjttiittttttttttttttttjjffjjttjjjjffffffffLLffffffjjjjjjjjjjjjjjttttttttttttttttttttiittttiiiiiittttffGGLLii;;;;;;;;;;,,,,,,,,,,,,,,,,,,,,,,,,,,,,
LLLLLLjjttiiiiii;;;;;;;;;;iiffffffjjjjjjjjffffttttttjjttiiiittttttttttttttjjjjjjttjjjjjjjjjjffffffffffffffffjjjjjjjjjjjjttttttttttttttttttttttttttiiiittttjjLLGGttii;;;;;;;;,,,,,,,,,,,,,,,,,,,,,,,,,,,,
LLffLLjjttiiiiiiii;;;;;;;;ttLLffjjjjjjffLLjjttttttttttttiittttttttttttttttjjffttttttjjjjjjjjjjjjjjffffffffffjjffjjjjjjjjjjjjttttttttttttttttttjjttttttttttjjLLGGffiiii;;;;;;;;,,,,,,,,,,,,,,,,,,,,,,,,,,
LLLLjjjjttiiiiii;;;;;;;;iittjjjjffjjffffjjjjjjttttttttttttttttttttttttttttjjttttttttttjjjjjjjjjjjjffffffffffffffffjjffjjjjjjjjjjttttttttttttttttjjttttjjttjjffGGLLtt;;;;iiii;;,,,,,,,,,,,,,,,,,,,,,,,,,,
LLffjjjjttiiiiii;;;;;;;;iijjjjffjjjjffjjjjjjttttttttttttttttttttttttttttttjjttttttttttjjttjjjjjjjjjjjjjjffffffffffffffjjffjjjjjjjjttttttttttttttjjjjttttjjjjjjGGGGttii;;iiiiii;;,,,,,,,,,,,,,,,,,,,,,,,,
LLLLffjjttiiiiii;;;;ii;;iiffffjjjjffjjjjjjjjttttttttttttttttttttttttttttttjjiittttttttttttttttjjjjttttjjjjffffffffffffffffjjffjjjjjjjjjjttttttttttjjjjjjjjjjffLLGGjjiiiiiiiiiiii;;,,,,,,,,,,,,,,,,,,,,,,
LLffffjjjjttiiiiii;;ii;;ttffjjjjffffjjjjjjjjttttttttttttttttttttttttttttjjjjiittttttttttttttttttttttttjjjjjjffffffffffffffffffjjffjjjjjjjjjjttttttffffffffffffffGGjjttiiiiiiiiii;;;;,,,,,,,,,,,,,,,,,,,,
LLLLffjjjjttiiiiiiiiiiiiffffjjffffjjjjjjjjjjttttttttttttttttttttttttttttjjttiittttttttttttttttttttttttttttjjffffffffffffffffffffffffffjjjjjjjjttffEEGGffffLLGGGGGGffttiiiiiittii;;;;;;,,,,,,,,,,,,,,,,,,
LLLLjjjjjjttiiiiiiii;;ttLLjjjjffffjjjjjjjjjjjjttttttttttttttttttttttttttjjiiiittttttttttttttttttttttttttjjjjffjjjjffLLffffffffffffffffffffffjjffEEKKEEGGffLLGGGGGGLLjjttiiiitttt;;;;,,,,,,,,,,,,,,,,,,,,