/*
;;;:::::::::::::::::::::::::::::::::::::::::::::::::::::::::;;;;;;;;;;;;;;;;;;;:::::::::::::::::::::;;;;;;;;;;:::::::::::::;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;++++
::::::::::::::::;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"
#define ll long long
#define ld long double
#define ff first
#define ss second
#define pii pair<int, int>
#define mp make_pair
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);
}
}
struct chash {
const double PI = acos(-1);
const uint64_t C = (2e18 * PI)+71;
const uint32_t random = chrono::steady_clock::now().time_since_epoch().count();
size_t operator()(ll x) const {
return __builtin_bswap64((x^random)*C);
}
};
const int N = 2e5;
const int R = 25000;
int big_region_id[R];
int reg[N];
int region_cnt[R];
int precalc[505][R];
vector<int> adj[N];
int timer = 0;
vector<int> region_node[R];
int from[N], to[N];
vector<int> in_reg[R];
void dfs_precalc(int u, int cnt, const int &pRegion){
int cur_reg = reg[u];
if (cur_reg == pRegion) {
// cout << u << ' ' << pRegion << ' ' << '\n';
cnt++;
}
precalc[big_region_id[pRegion]][cur_reg] += cnt;
//int tmp = (cur_reg == pRegion);
for (const int &v : adj[u]){
dfs_precalc(v, cnt, pRegion);
}
}
void dfs(int u){
from[u] = ++timer;
region_node[reg[u]].push_back(timer);
in_reg[reg[u]].push_back(u);
for (const int &v : adj[u]){
dfs(v);
}
to[u] = timer;
}
int main(){
setIO();
int n, r, q;
cin >> n >> r >> q;
int big = sqrt(n) + 1;
memset(big_region_id, -1, sizeof big_region_id);
memset(region_cnt, 0, sizeof region_cnt);
memset(precalc, 0, sizeof precalc);
int first_reg;
cin >> first_reg;
reg[0] = --first_reg;
region_cnt[first_reg]++;
for (int i = 1; i < n; i++){
int p, rr;
cin >> p >> rr;
adj[p-1].push_back(i);
reg[i] = --rr;
region_cnt[rr]++;
}
int cnt = 0;
for (int i = 0; i < r; i++){
if (region_cnt[i] >= big) big_region_id[i] = cnt++;
}
for (int i = 0; i < r; i++){
if (big_region_id[i] != -1) dfs_precalc(0, 0, i);
}
dfs(0);
for (int i = 1; i <= q; i++){
int r1, r2;
cin >> r1 >> r2;
r1--; r2--;
if (big_region_id[r1] != -1) cout << precalc[big_region_id[r1]][r2];
else {
int ans = 0;
for (const int &u : in_reg[r1]){
//cout << u << ' ';
ans += (upper_bound(region_node[r2].begin(), region_node[r2].end(), to[u]) - lower_bound(region_node[r2].begin()
,region_node[r2].end(), from[u]));
}
cout << ans;
}
cout << '\n';
}
//for (int i = 0; i < r; i++)cout << big_region_id[i] << ' ';
}
Compilation message
regions.cpp: In function 'void setIO(std::string)':
regions.cpp:138:9: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
138 | freopen((s+".in").c_str(), "r", stdin);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
regions.cpp:139:9: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
139 | freopen((s+".out").c_str(), "w", stdout);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Execution timed out |
8 ms |
57936 KB |
Time limit exceeded (wall clock) |
2 |
Execution timed out |
7 ms |
57936 KB |
Time limit exceeded (wall clock) |
3 |
Execution timed out |
8 ms |
57936 KB |
Time limit exceeded (wall clock) |
4 |
Execution timed out |
8 ms |
57936 KB |
Time limit exceeded (wall clock) |
5 |
Execution timed out |
10 ms |
58192 KB |
Time limit exceeded (wall clock) |
6 |
Execution timed out |
8 ms |
58192 KB |
Time limit exceeded (wall clock) |
7 |
Execution timed out |
9 ms |
58192 KB |
Time limit exceeded (wall clock) |
8 |
Execution timed out |
8 ms |
58192 KB |
Time limit exceeded (wall clock) |
9 |
Execution timed out |
9 ms |
58448 KB |
Time limit exceeded (wall clock) |
10 |
Execution timed out |
13 ms |
58448 KB |
Time limit exceeded (wall clock) |
11 |
Execution timed out |
11 ms |
58704 KB |
Time limit exceeded (wall clock) |
12 |
Execution timed out |
11 ms |
59216 KB |
Time limit exceeded (wall clock) |
13 |
Execution timed out |
14 ms |
58704 KB |
Time limit exceeded (wall clock) |
14 |
Execution timed out |
15 ms |
59216 KB |
Time limit exceeded (wall clock) |
15 |
Execution timed out |
16 ms |
61776 KB |
Time limit exceeded (wall clock) |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Execution timed out |
47 ms |
61768 KB |
Time limit exceeded (wall clock) |
2 |
Execution timed out |
38 ms |
60744 KB |
Time limit exceeded (wall clock) |
3 |
Execution timed out |
29 ms |
63568 KB |
Time limit exceeded (wall clock) |
4 |
Execution timed out |
14 ms |
59472 KB |
Time limit exceeded (wall clock) |
5 |
Execution timed out |
19 ms |
61008 KB |
Time limit exceeded (wall clock) |
6 |
Execution timed out |
84 ms |
60488 KB |
Time limit exceeded (wall clock) |
7 |
Execution timed out |
92 ms |
61256 KB |
Time limit exceeded (wall clock) |
8 |
Execution timed out |
101 ms |
65776 KB |
Time limit exceeded (wall clock) |
9 |
Execution timed out |
44 ms |
65728 KB |
Time limit exceeded (wall clock) |
10 |
Execution timed out |
172 ms |
70492 KB |
Time limit exceeded (wall clock) |
11 |
Execution timed out |
58 ms |
65080 KB |
Time limit exceeded (wall clock) |
12 |
Execution timed out |
79 ms |
66632 KB |
Time limit exceeded (wall clock) |
13 |
Execution timed out |
59 ms |
66632 KB |
Time limit exceeded (wall clock) |
14 |
Execution timed out |
218 ms |
66480 KB |
Time limit exceeded (wall clock) |
15 |
Execution timed out |
59 ms |
70984 KB |
Time limit exceeded (wall clock) |
16 |
Execution timed out |
67 ms |
76272 KB |
Time limit exceeded (wall clock) |
17 |
Execution timed out |
106 ms |
75080 KB |
Time limit exceeded (wall clock) |