/*
;;;:::::::::::::::::::::::::::::::::::::::::::::::::::::::::;;;;;;;;;;;;;;;;;;;:::::::::::::::::::::;;;;;;;;;;:::::::::::::;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;++++
::::::::::::::::;S*.......+%:,....,*%,......,S+,,:;*%+:,..........,:*S##+.......+#SS:.......?@*.............%S:....;%;.....,%?%?,.....*%+?*:,,........,,:;?*,+S,......,S#?.......;S;....................
:::;;;::::::::::+S*.....,.+S;,,...,*%,......:S?;+*%S;......:?*,......+#@%,......:##S......,,S@*.......,,,,::%#?;,..,*%:.,...*#S;...,.;S*%*,.....,*%;......,%?*S,......,S#?.......;S;....................
::::::::::::::::+S*.......+S;,,...,*%,......:#%???#?.......+@@;......,%@#;......,%@*.......;##*.......+#%%%%%%%?+,..,?%,.,..:#S,....:S?*%:.,....,S@?.,.....+S?S,......,S#?.......;S;....................
;;;;;;;;:::;;;::+S*.......+S;,....,*%,......:#S??%#?.......+@#:.......%##*,.....,%@+......,?##*.......*#S%%%???%%*:,.:%*...,,?+....,%?:*%,......,S#*.,.....+S?S,......,S#?.......;S;....................
;;;;;;;;;;;;;;::+S*.......+S;,...,,?S,......:#S%%%#?.......+@@:.......%##S,......*#:......,SS#*......,:;;;;+S%??%%?:.,+S;...,,,....*S:,*S,......,S#*.......+S?S,......,S#?.......;S;....................
;;;;;;;;;;;;;;::+S*.......+S;,,,,,:?S,......:#S%%%#?.......+@@:.......%#S#;......;#:......;#S#*............:#%????%%;,,*S:.,......;S+,,*S,......,S#*.......+S?S,......,S#?,......;S;....................
;;;;;;;;;;;;;;::+S*.......+S;,,,:;+%S,......:#S%%%#?.......+@@:.......%#%#?......:*,......?#%#*.......:++++*S??????%%+,:%?,......:%*,.,*%,......,S#*.......+S?S,......,S@?.......;S;....................
;;;;;;;;;;;;;;::+S*.......+S;::;+*?SS,......:#S??%#?.......+@@:.......%#?%S:.....,+......:SS%#*......,*#%???****????%%*:;S;......*S:..,*S,......,S#*.......+S?S,......,S@?.......;S;....................
;;;;;;;;;;;;;;::+S*.......+S;:+???%#S,......:##%%%#?...,...+@@;......,%#?%#+.....,,......+#??#*.......+#%%%??****????%%?*S;......*%:..,*%,......,#@*.......+S?S,......,S@?.......;S;....................
;;;;;;;;;;;;;;::+S*.......+S*?%%?%%#S,.....,,:;::+#S:..,,.,:%%:..,,..;#%??#%,............?#??#*.......,:;;;;*S?****????%S#;......*%:...;S+......,?S+.,....,%?+%+.....,,?S+,.....,*%:....................
;;;;;;;;;;;;;;:;+S*.......+#%%%%%%S#S,...........:##%;,............,+S%?*?%#;...........:#S??#*.............+#?*****????S#;......*S:...,+%*:,...........,:??:,+%+:,...........,:*?;,....................
;;;;;;;;;::;;;::+%?;;;;;;;?#S%%%SSS#S;;;;;;;;;;;;*S%%SS?+;;::::;;*?%S?*****S?;;;;;;;;;;;*S%??%?;;;;;;;;;;;;;*S?******???%S*;;;;;;*?,....,:+**+;;:::::;+***;,..,:+**++;;::::;;+**;,......................
:::::;;;;:;;;;:;;;+++++*%SSS%%%SSSSS%S##SS%%%%%SS%??%%%%%SSSSS%%%%???****+**??????%%???%?++*?**????%%%***????*********???%%SS?+;;:,,.......,,:;++++++;;:,........,,:;;++++++;:,,........................
;;;;;;;;;::;;;;;;::,::;?%%%S%SSSSSS%SSSS%?????%%???%%???%%%%%%??%??%%*****??****+++*+++*?+++*?*++++*?*+;;;++***********??????*;,........................................................................
;;;;;;;;;;;;;;;;:::::+?%SSSSSSSSSS%SS#SS%%???%S%?%S%%?%%%%%%???%?*?%%***????????**???***??***??*****???*++;+**************+;:;++:,......................................................................
;;:;;;;;;;;;;;;:::;;+%SSSSSSSSSSSSS###SSS%%%%S%?%SS%%%%%%%???**??**%%?*???%?????????%?**?%?**?%?*?***%?***+;+*******++;:,,,,::;;+;,.....................................................................
;;;;;;;;;;;;;;:::++*%SSSSSSSSS##SS#S#SSSS%%%S%%%SS%%%%%%????*:++?**%%?????%%?%%%%%??%????%????%%????*?%?***;;++;;;::,,,..,,,,::;;+;:....................................................................
::;;;;;;;;;;;::;+*?%SSSSSS######S####SSSS%%SS%%%%%%%SS%??%?+,,*;?**?%%????%%?%%%%%%%%%???%????%%??????S%?**+:,,,,........,.,,,:::;++:,..................................................................
;;;;;;;;;;;::;+*?%%S###SS############SSSS%%#S%%%%SSSS%%?*+;:::*;????%%???%%%%?%%%%%%%%%??%????%%%?????%%???*;,.............,,,,,::;;+;,.................................................................
;;;;;;;;;;::+*?%%SS##################SSSS%S#S%%%SSSS%?*;:,.,,,*;+%%%%S%???%%%%%%%%%%%%%??%%???%%%%????%S%??*;:...............,,,,::;;++:,...............................................................
;;;;;;;;;;+++*SS%SS#################SSSSSSS#S%%%SSSS?*+;;::,,,:;:*S%SSS%??%%%S%?%%%?%%S%?%%????%S%????%S%??*;:...............,,,,,:::;++:,,,............................................................
;;;;;;;+**+;+?SS%SS#################SSSSSSS#S%%%S#S%S###SSS?+;::::*%SSSS%%%%%%S%?%%??%%%?%%????%S%????%S%%?*;:................,,,,,:::;;+;,.............................................................
++++++******?S##SS##################SSSSSSS#S%%SSS+;S#SS######%*;::;?SSSS%%%%%%S%%%%??%%%%%????%SS????SS%%?*;:,.................,,,,,::;;++:,...........................................................
******??????%S##SS##################SS#SSSS#SS%SS%:;%?%SSS#SS?*?%+:::+%%SSS%SS%%SS%%%%%%%%%????%SS???%SSS%?*;:...................,,,,,:::;++;,..........................................................
?????????????S##SS##################SS#SSSS##S%SS?::++;++?%?;:::+;:,,,:+??%SSSS%%%SSSS%%S%%???%SSS???%SS%??+;:....................,,,,,:::;;+;:.........................................................
%????????????%##SS###################S#SSSS##S%SS?;::;++;;::,:::,:,,,,,,;+++??%SS%?%SSS%SS%???%S#S%??SSS%?*:,,......................,,,,,::;;++:,.......................................................
%%%%%%%%?????%S######################SS#SSS##SSSS?;:::::::::,:,,,,,,,,,,,:;;+?SS##S%%SSS%%%??%S##S??%SSS%?+,,........................,,,,,::;;++;,......................................................
????%%SSSSSSSSSS#####################SS#SSSS#SSSS%;::::::::::::::,,,,,,,,,,+%S%SSS%+:;?#SS%?%S###%??S%SS%?;,,.........................,,,,,:::;;+;:.....................................................
????????%%%SSSS#######################SSSSSSSSSSSS*:::::::::::::::,,:::::::++++++;:::;***%%?%S##S%%%%*S%%?:,..........................,,,,,,:::;;++:,...................................................
?????????????%%%SSSSS##################SSSSSSSSSSSS;,::::::::::::::::::::::;;;:::,,,:+*%SS%%S###S%%%*%?%?:,..............................,,,,,:::;+++:..................................................
????????????????%%?%%SSSSS#SS##########SS#SSSS#SSS%*:::::::::::::::::::::::::::;:::;*S##S%%S####S%%?%*+;,.................................,,,,::::;*%?;,,...............................................
??????????????????%??%%%%%%%%#######%%####SSSS###SS*+;:::::::::::::::::::::::::::;?S####SS######SS%S*,,...................................,,,,,,:;*?%%%+,,,.............................................
%%%%%%%%%%%?%??%???%%?%%%%%?%S#S%%%%%?S####SSS%S###S+:;::::::::::::::::::::::::;?S#####%S#######S?*;,......................................,,,,;+*???%%%?;,.............................................
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%S#S%???%??%####SSS%S###S+::::::::::::::::::::;;+?%######S?%#####S%+:,.......................................,,::++*??????%%%%+,............................................
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%S%%%%%%%%%S#####SS%SS##S*;:::::::;;;;;++**?%SS########%*%#####?:.....................................,,,,::;++******?????%%%%*:,,.........................................
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%SSS#####S%%%S##S%*++**?++**%SSS############S?*%####?:,..................................,,,::;;++***********??????%%%%;,.........................................
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%SSSSSSSSSS%%S###S%%??%S#S%?%%%%%*??*SSSSS##########?+?###?:............................,,,,,,:::;++++*****************??????%%%*:........................................
%%%%%%??%???????%%%%%%%%SSS########SSSSSSS%SS###S%%???%SS%???%%%+%%?S%%%#########?+%#S?:,.....................,,,,,,:::;;;+++++++********************???????%%%?;,,.....................................
%??????????????%%%SSS#################SSSSSSS####S%%%%%%SS%%%%%%?*%????%########%*%?;:,.......,,,,,,,,,,,::::;;;;+++++++++++++++++*+++*****************??????%%%%+,.....................................
????????????%%SSSSSSSSS%%%%%%%%%%%SSSS###SSSSS#S###SS%%%%S#S%??*?**?%??S####S%SS??*;;;;;;;;;;;;;;;;+++++++++++++++++++++++++++++++++++++****************???????%%%?;,...................................
???????%%%%SSSSS%%%%%%%%%%%%%%%%%%%%%%%SS%???%%%?%%S%?****%#%+;+*?*??%?%###S?*?********************+*++++++++++++++++++++++++++++++++++++****************????????%%%+,..................................
?%%%%%SSSSSSSS%%????%%%%%%%%%%%%%%%%%%%%%*++++++++*?%%?*+;+%#%+++??*???%##S???*?**************+++++++++++++++++++++++++++++++++++++++++****+***************???????%%%*:.................................
+*?%%SSSSSSS%%%?????%%%%%%%%%%%%%%%%%%%%?+;;;;;;+++++**???**%#*;;+%***?S##%???*?**************+++++++++++++++++++++++++++++++++++++++++****+***************????????%%%?;,...............................
;++*%SS%%S%%???%???????%%%%%%%%%%%%%%%%%?+;;;;;:;;;;;;;;;;;;+S*;:;??*+?#S%??????**************++++++++++++++++++++++++++++++++++++++++++++*+*****************??????%%%%%*:,.............................
;+*%S%%%%%%%????%%%%%%%%%%%%%%%%%%%%%%%%?+;;;;;;;;:::::;;;;;;?*;++*?*+*#S???????**************++++++++++++++++++++++++++++++++++++++++++++*+******************????????%%%?;,...................,,,,,,:::
;+%%%%%%?????????????%%%%%%SSS%%%%%%%%%%%*;;;;;;;;;;;::::::::+;;;;+??**S%???????***************+++++++++++++++++++++++++++++++++++++++++++*+********************???????%%%?;,........,,,,,,:::;;++++++**
:?%%%%%%%%%%?????????%%%%%%%%%%SSSSS%%%?%?+;;;:;;;;;;;::::::;;:::::;?*+%S%???????**************++*+++++++++++++++++++++++++++++++++++++++++++*++******************????????*++:,,:::;;;+++++*************
;%%%%%%%%%??????**????????%%%%%%%%%%SSSSSS*++;;;:;;;+;;:::::::::::::;?*?%%??????***************++++++++++++++++++++++++++++++++++++++++++++++*++*******************??????+;;+++++*************+*********
+%%%%%%%%%%???********???????????%%%%%%%%S%*+;++;;:;;+;::::::::::::::+??%%?????******************++*++++++++++++++++++++++++++++++++++++++++++++*********************??*;::;;;+*************++++********
?%%%%%%%%%%?*******?????%%%%%?***??????%%%%%*;;;;;;;;;;;::::::::::::::*?%%?????******************++*++++++++++++++++++++++++++++++++++++++++++++**********************;:,:::;;;++***********+*++********
%%%%%%%%%%%?********??????%SSSS%??****?????%%?+;;;;;;;;;::::::::::::::;?%%?????********************++++++++++++++++++++++++++++++++++++++++++++++*****************++:,,,,,::::;;++**********************
%%%%%%%%%%%%?*******????????%SS#S%%???***?*?%%*+++;;;;;;::::::::::::::;?%%?????********************+++++++++++++++++++++++++++++++++++++++++++++***************++;:,,,,,,,,,:::;;++*********************
%%%??%%S%%%%??*****????????????%S##SS%%?????%S%+++;;+;;:::::::::::::::;*%%?????********************+++++++++++++++++++++++++++++++++++++++++++++***********++;:,,,...,,,,,,,,:::;;;++*******************
%%%???%SS%%%%??****??????????????%S###SS%%?%SS%+++;;;;;::::::::;;;;;::;*%%???????*****************+**++++++++++++++++++++++++++++++++++++++++++++******++;::,,..........,,,,,,,:::;;;+******************
??????%SS%%%%%??*****???????????????%S###S%SSS%+++;+++;:::::::::;;;;::;*%%??????********************++++++++++++++++++++++++++++++++++++++++++*+**+;::::,,,,,,,,........,,,,,,,::::;;;++****************
???????%SS%%%%%???***??????????????????%S####S?+;++++;::::::::::;;;;::;*%%?????***********************++++++++++++++++++++++++++****++++++********?*;:..,.,,,,,,,,,.......,,,,,,,::::;;++**********++***
????????%SS%%%%%??****????????????????????%SSS?++*++;:::::::::::;;;;::;;+**?????***********************++++++++++++++++++++++*?????%??*************???;,,.,,....,,,,,,,,....,,,,,,,:::;;;++********+++*+
?????????SSS%%%%%??*****?????????????????????%%?*+++;::::::::::;;;;;::;;;;:;++*******************+++++*+++++++++++***********?%%%%??%%?**************??+,,,.....,,,,,,:,,...,,,,,,,,::::;;++*?*+***++++*
?????????%SSS%%%%%???******????????????????????%?++;:::::::::::::;;;::;;;;:::,,,::;;++++++***+*****+****+++++****************?%S%%????%?*************???+,......,,,,,,,,,,,,,..,,,,,,::::;;;+??**+*++++*
%?????????%SSS%%%%%%???*******????????????????????+:::::::::::::::;;::;;;;:::,,,,,,,,,,,,,,,:::::::::::::;+**??***************%S%%%????%??????????????%??;....,,,,,,,,,,,:::::,,,,,,,,,:::;;+?%?***+**++
%%???????*?%S#S%%%%%%%??***************????????????+::;;;;;::::::::::::;;;:::,,,,,,.,,..............,:;+***?*****************?%S%%%?????%%%%????????????%*,.,,,,:::::::,:::;;;;:,,,,,,,,::::+?%%??*+*+++
%%%??????**?S##S%%%%%%%???*************************?*+;;;++;:::::::::::;;;:::,,,,,,............,,:;+*???*?******************?%%%%%%?????%%%%?*****???????*:,,,,,,,,,:::::::::;;;:,,,,,,,,,::*??%%%?***++
?%%%????**?%%SS#S%%%%%%%????***********************???*;;+;;;::;;;;;++;;+;:::,,,,,,.........,,;+*????????%%%%????**********?%%%%%??***?%%%%%?*******?????*;;;:::,,,,::::;;:::::::,,,.,,,,,:+?????%%?**++
??%%%????%??*?SS#SS%%%%%%%???**********************???%*++;;;;+++++++++++++;:,,,,,,.......,:+*????????%%%%%%%%%%%%????????%%%????****??%%%%%%?******??*+;:,,,......,,,,,:::::,,...,.....,;**?????%%%?***
S??%%%%%%??????SS##S%%%%%%%?????******************??%SSS%??*+++++++++++;;;++:,,,,,,.....,;*???????????????%%%%%%%%%%%%%??%????******???%%%%%%????*+;:,,..............................,,:+*??????????%?*+
%%??%SS%????????S###S%%%%%%%????***************?%%SSSS%%%%?????*++++++;:;++**+;,,,,..,:*??????????????????%%%%%??%%%%%%??????******?%????%%%?+;:,,.................................,,:+********???????*+
%??*%%%%%????????%S##S%%%%%%%???***********??%%S%%%%%???%SS%?***?**+++;+**???%%?*+::;*%%?????????????????%%%%%%%%%%%%?????????****????????*;,....................................,:;+***********??????*+
;;*?????%%%???????%S##S%%%%%%%?******?????%%%%?????????%%##S??***?????????%%??%%SSSSS%??????????????????%%%%%%%%%%%%%??????????**?????%??+,..................................,,,:;+****************??**+
;;+??????%%%%??????%S##SS%%%%%%?***??????????????????%%%%###%???***?????%SS%?%%SS#S%????????????????????%%%%%%%?????%??????????????%??*;:,,...............................,,,:;+**********************++
;;;**??????%%%%?????%S###S%%%%%????????????????????%%%%%%###S%????????%SSS%??%S#S%?????????????????????%%%%%%%?????????????????????*;:,..............................,,,,:;++************************+++
;;;++??????%%%S%??????%S##S%%%%%%%%%?????????%??%%%%%%%%S###%%%%%%%?%S###S%%%SSS%?????????????????????%%%%%%%%???????????????%%%?;,,..............................,,::;+++***************************+++
;;+++**?????%%%SS%?????%S##SS%%%%%%%%?%%%%%%%%%%%%%%%%%%S##S%%%%%%%%S####SSSSS%???????%%%????????????%%%%%%%?????????????%%%?*+:,...........................,,,,:;;+++***++************************+++++
+++++***???%%%%%%SS%%????%S##S%%%%%%%??%%%%%%%%%%%%%%%%%S##%%%%%%%%S####SSS%%????????%SS%??????????%%%%%%%%%?????????%%%??*;,,........................,,,,::;;++++***+++*+++*********************+++++++
****?*?*??%?%%%%%%SSS%%???%S###S%%%%%%??%%%%%%%%%%%%%%%S###%%%%%%%S####SS%%?????????%SSS%??????????%%%%%%%??????%%???*+;:,.....................,,,,,::;;++++++++++++++++****+******************+++++++++
***++++;;+*??%%%%%%SSSSS%???%S###S%%%%%%?%%%%%%%%%%%%%%S##S%%%%%%S####S%???????????%SSS%%?????????%%%%%%%????%?*+;:,,.................,,,,,:::;;;++++++++++++++++++++++++++*+++*************++++++++*+++
;;;::;;;;;;+*??%%%%%%SSSSS%???S###S%%%%%%%%%%%%%%%%%%%%S##S%%%%%S###S%????????????%SSS%%%????????%%%%%??????*+:,...,,,,,,,,,,,,:::::;;;;+++++++++++++++++++++++++++++++++++*++***+*******+++++++++++++++
:::;;;;;;;+++**???%%%%%%SSSS%%?%S###S%%%%%%?%%%%%%%%%%%##S%%%%%%S##S%????????????%SSS%%%????????%%%%%????*+;;;;;;;;;;;;;;+++++++++++++++++++++++++++++++++++++++++++++++++++++***+++++++++++++++++++++++
:::;;;++****+++++*???%%%%%%SSSS%%%S###S%%%%%%%%%%%%%%%S##S%%%%%S#S%????????????%%SSS%%%????????%?%%%%??**++*****++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
;;++*****+++;;+++++**???%%%%SSS#SS%SS##SS%%%%%%%%%%%%%S#S%%%%%%SS%????????????%SSS%%%%?????????%%???**+****++*++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+***++++;;;;;;;++++++++***??%%%SS##SS####S%%%%%%%%%%%SSSS%%%%%%%?????????????%%%%%%%????????????***++++*****++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++;;;++;;;;;;;;+++++++++++++***??%%SS######S%%%%%%%%%SS%%%%%%%%????????????%%%%%%%??????????*****************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
;;;;;;+++;;;;;+++++++++*************??%%SS###S%%%%%%%%%%%%%%%%???????????%%%%%%%%???????*******************+**++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++;;++++++++++
;;;;;;;++++;;++++++++++++++++***********??%SS##SS%%%%%%%%%%%%??????%%%%%%%%%%%%??%%%%??******************++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++;;;;+;+++++++++++
;;;;;;;;;;+++++++++++++++++;;;;;++***?%%%%%%%%S%%%%%%%%%%%%%%%%%%%%%%%%%%?%??????????????????********************+*+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++;+;+;;++++++++++++++
;;;+++;;;;;+++++++++++++++*****??%%%%%???****++++++**??%%%%%%%%%%%%%%%%???**++;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++;;;;+++++++++++++++++++
;;;;;;;;;;;;;++++++++++**????%%%??***+++;;;;;;;;;::;;;;;+++****????***++;;;;;:::;;;;::::::::::::::::::::::::::::::::::::;;;;;;;;;;;;;;;;+;;;+++++++++++++++++++++++++++++++++;;;;;;;;;++++++++++++++++++
;;;;;;++++++;;;;+++**?????%??*++;;;;:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::;;;;;;;;;+++++++++++++++++++;;;;;;;;;;;;;;;++++;+++++++++++++
;++++++++++++++**?????%??*+;;;;:::::::::::::::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,:::::::::::::::::::::;;;;++++++++;;;;;;;;;;;;;;;;;;+;;;;++++++++++*+***
;;;++++;;+++*??????%%?*+;;::::::::::,,:,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,::::::::::::::::::::::::::::;;;;;+++++;;;;;;;;;;;;;;;+++++*********???
+++++;;+**??????%%?*;;:::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,::::::::::::::::::::::::::::::::::::::;;;;+++;+++++++*****?????????????
++;++*???????%%?*;:::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,:::::::::::::::::::::::::::::::::::::::::::::;+****??????????????????????
;;+*??????%%?*+;::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,::::::::::::::::::::::::::::::::::::::::::::::::::;*????????????????????????
+???????%%?+::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,::::::::::::::::::::::::::::::::::::::::::::::::::::::::;*??????????????????????
??????%%*;::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,::,,,:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::,,,,,,,:::::::::+*?????????????*****++
?%??%?+;:::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::;;;;;;;;;;;;;;;;:::,,,,,,,,,,:::::::::;+??****++;;;::,,,,,,
%?%?+::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::;::;;;;;;;;;;;;;;;++;;;;;;;;;::::,,,,,,,,,,,,,,,,,,,::::::::+:,,,,,............
?%*;:::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::;;;;;;;;;;;;;;;;;+++++++++;;;:::::,,,,,,,,,,,,,,,,,,,,,,,,,,,::::::::;,.................
%+::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::;;;;;;;;;;;;;++++++++++;;;::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,::::::::;,.................
*:::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::;;;;;;;;;;;;;+++++++++++;;;:::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,::::::;:..................
:::,,,,,,,,,,,:,,,,,,,,,,,,,,,,,,::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::;;;;;;;;;;;;;;;+++++++****++;::::::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,:::::;;,..................
:::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,::::::::::::::::::::::::::::::::::::::::::::::::::::::;;;;;;;;;;;;;;;;;;;;+++++++****++;;::::::,::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,:::;;,...................
::,,,,,,,,,,,,,,,:,,,,,:,,,,:::::::::::::::::::::::::::::::::::::::::::::::::::;;;;;;;;;;;;;;;;;;;;;;;+++++++*****++;::::::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,::::,,....................
,,,,,,,,,,,,,,,,,,,,,::::::,,:,:::::::::::::::::::::::::::::::::::::::::::::;;;;;;;;;;;;;;;;;;;;;;++++++********+;:::::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,:::;;:,......................
:::::,,,::::::,,:::::,::::::::::::::::::::::::::::::::::::;;;;;:::;;;;;;;;;;;;;;;;;;;;;;;;;;;+++++*****???***+;::::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,:,,,,,:::::;;;;:,,......................
******++******?******+;:::+**?****?**;::::::;**?????**+***????*****???????*??????????????*+*????%%%%??%?????***+:,,,,,:+**********+::+******+:,,,:+***************++******????*****+++++********++:,....
,,,,,*##;,,,,,S+,,,,;S*:+??;:,,,,,,:+??+:::;?%:,,,,,,%#S:,,,,,,?#S,,,,,,,,,S#;,,,,,,,,::;?SS%,,,,,*S?S*,,,,,,,;S+:,,,,+S;,,,,,,,::;?%S:,,,,+S;,,:*S:,,,,,,,?#:,,,:S#?,,,,?@;,,,,,,,,*@?,,,,,,,,::;?*:...
,....;@S,....;#;....:S*;%?,..,,%?,...,%%;::;?S,......+@?.......?@S,....:+++S#;....:?+....,S@S,....*S%S:..,:,..,%%:,,,,+S;....:?:...:##:....;S+,,;%?,..,:,..;@%,..,%@;...;##;....,++;*#?.....*?,...,%*,..
+....:#?,....*@;....:S*+S+....,#S.....*S+::;?S,...,,.:S;.,:....?@S,....*@S%%#;....:@%.....?@%,....*SS?,..,;:.,.+S+,,,,+S;....;#;...,##:....;S+,:+S;...,+,..,%@*...+%,..:%%S;....:#S*+%?.....%@,....%?,..
%,...,S*....,S@;....:S*+S*....,SS+++++??;::;?S,...+;.,+,.:+....?@S,....,;:+##;....:#?.....?@S,....*#S+..,,%*.,,,%?:,,,+S;....:+,...:##:....;S+::?%,...;S:,,.+##+..,:,.,%?+S;....,:::%#?.....;;,,,:+%;,..
#;....+;....;##;....:S*+S*....,SS%%%%%*+;::;?S,...+*..,,.+*....?@S,...,:;:+##;....:#?.....?@S,....*#S:...,S?,.,.+S;,,,+#;....,,::;+?SS:....;S+:;S*....+@;.,.,%SS:.....*%:;S;....,:::%#?.....;;,,,;?%;...
#*....;:....*##;....:#*+S+....,SS,,,,,*%;;:;?S,...+%,...,%*....?@S,....*#?*?S;....:@?.....?@%,....*@?,...,++,.,.,S*:,,+S;....:S%**+;*S:....;#*;*S;....;*:..,.*SS*....:S+,;S;....;#%+;%?.....%#,...,%?,..
SS,...,,...,SS#;....:??*#*....,S%.....?%;:;;%S,...+#;.,.:#*.,..?@S,....+%?*?#;.,..:S*.....?#%,....*@+...,,::,....?%:,,+S;....:S+:,,:*S:....;%?*S%,...,:::,...:##?....:S+,;S;....:??*+S?.....%#,....%?,..
%#+........+#S#;.......,S#+,...::..,:*S?+++*SS,...+@*...;@*....?@%,........+@;....,,,....:%S%,....*S,....*##+....;S+,,+S;....:S+::::*S:.......,#*....,S#%,...,?@?....:S;.;S;........:#?.....%#,....%?,..
%SS********%#S#?********S##S?*++++*?SS%?????%S****?#S***S#%****%SS*********?#?*********??%?*%*****%S*****%%%?*****%*;;+%?****?%*;+;+*S?********#?****?S%%*****%#S*****%+:;%?*********S%*****%S*****%*:::
*/
#include"bits/stdc++.h"
#pragma GCC optimize("O3", "unroll-loops")
#define ll long long
#define ld long double
#define ff first
#define ss second
#define pii pair<int, int>
#define mp make_pair
#define make_rng mt19937 rng(chrono::steady_clock::now().time_since_epoch().count())
#define make_rng64 mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count())
using namespace std;
void setIO(string s = ""){
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
if (!s.empty()){
freopen((s+".in").c_str(), "r", stdin);
freopen((s+".out").c_str(), "w", stdout);
}
}
const double PI = acos(-1);
struct chash{
const uint64_t C = uint64_t(2e18 * PI) + 71;
const uint32_t random = chrono::steady_clock::now().time_since_epoch().count();
size_t operator()(uint64_t x) const {
return __builtin_bswap64((x^random)*C);
}
};
double ans[100000];
double get_r(double ax, double ar, double bx){
double n = (bx - ax)*(bx - ax);
double d = ar*4;
return n/d;
}
int main(){
setIO();
int n;
cin >> n;
stack<pair<double, double>> balls;
for (int i = 1; i <= n; i++){
double x, r;
cin >> x >> r;
double maxR = r;
while (!balls.empty()){
pair<double, double> p = balls.top();
double cur = get_r(p.ff, p.ss, x);
maxR = min(maxR, cur);
if (maxR >= p.ss) balls.pop();
else break;
}
ans[i-1] = maxR;
balls.push(mp(x, maxR));
}
cout << fixed << setprecision(3);
for (int i =0; i < n; i++) cout << ans[i] << '\n';
}
Compilation message
bal.cpp: In function 'void setIO(std::string)':
bal.cpp:140:9: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
140 | freopen((s+".in").c_str(), "r", stdin);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
bal.cpp:141:9: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
141 | freopen((s+".out").c_str(), "w", stdout);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
1 ms |
344 KB |
10 numbers |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
1 ms |
344 KB |
2 numbers |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
1 ms |
344 KB |
505 numbers |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
2 ms |
348 KB |
2000 numbers |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
13 ms |
1128 KB |
20000 numbers |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
34 ms |
2132 KB |
50000 numbers |
2 |
Correct |
27 ms |
2136 KB |
49912 numbers |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
65 ms |
3608 KB |
100000 numbers |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Runtime error |
35 ms |
3952 KB |
Execution killed with signal 11 |
2 |
Halted |
0 ms |
0 KB |
- |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Runtime error |
30 ms |
3924 KB |
Execution killed with signal 11 |
2 |
Halted |
0 ms |
0 KB |
- |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Runtime error |
29 ms |
3776 KB |
Execution killed with signal 11 |
2 |
Halted |
0 ms |
0 KB |
- |