=~~~~~~~~~~~===++++===~~~=======~~===+++^^^^^^^^^^^^^^^^^^^^^^^^^^+++===~~---:..······............··.......::::----~~~=~~----:::::...·····.::----~~~~~~~~~~~~~~~~~~~~~~==+++++++======+===~~~~~~~~~--::......:::::---------:::::::::::::::::::-- ===~~~~~~~~==========~~~=============++++^^^^^^^^^^^^^^^^^^^^^^^^++++===~~--::...····...................::::::----~~~~~~~----::::::..·····..::------~~~~~~~~~~~==~~~~~~===+++++==========~~~~~~~~~----::...::::::---------::::::::::..::::::::-- ++==============~~~~~~~~===++++======++++++++++++^^^^^^^^^^^^^++++++====~~--:::............·····....::::-----------~~~~~~------::::...····....::::::----~~~~~~========================~~~~~~~~~-----------:::::----------:::::::::::......::::-- +++++++++++===~~~~~~~~~~==+++++++================++^^^^^^^^^^++========~~---::::::..:::::..······..:::---~~~~~----~~~~~~---------:::...···........::::--~~~~~~==========~~~~~=======~~~~---------------------------~~~~--:::::::-:::......::::-- ^^^^++++++===~~~~~~~~~~===++++++++===========~=====++++++++++=========~~~-------:::::::::..·······..::--~~~~~~~~~~~~~~~~~~--------:::...............:::---~~~~~~~~~~~~~~~~~~~~~==~~~~----::::::-------~~~~~~----~~~~~~~~---::::--:::::::::::::-- ^^^+++++===~~~~~~~~~==========++++++========~~~================~~~~~~~~~~~-------------::..·· ··..::--~~==============~~~--------::..···...........:::----------~~~~~~~~===~~~~~----:::::::::::::---~~~~~~~~~~~~~====~~----:::::::::---------- ^^++++====~~~~~~~~~~===========+++++======~~~~~~~~~~~~~~====~~~~~~~~~~~~~~~~~~~~~~~~~---::.··· ··..::--~~==============~~~--------::..····...........:::--------------~~====~~~----::::........:::---~~~~~~~~~~~~======~~----::::::------------ ++++++===~~~~~~~~~~~~==================~~~~~~~~~~~~~~~~=====~~~~~~~~~~~~~~~~~~~==~~~~~~--::..····...::--~~~===========~~~~--------:::....·..............:::::----------~~~~=~~~~~~---::::......:::----~~~~~~~~~~~~=====~~~---------------------- +++++++==~~---~~~~~~~~~============~~~~~~~~~~~~===============~~~~~~~---~~~===========~~~--:.......:::--~~~~~~~~~~~~~~~~-------::::::............·····.....::-----------~~~~~~~~=~~~---::::::::::-----~~~~~~~~~~~~~~~~~~-------------------~~~~- =++++++=~~-----~~~~~~~~~==========~~~~~~~~~~=========++========~~~~~~--~~~==============~~--:::.:::::---~~~~~~~~-------------::::....::::.......·········...::-----------~~~~~=====~~-----:::::----~~~~-------------------:::---~~--------~~~~~~ ===+++==~~~~----~~~~~~~==========================++++++++++========~~~~~===============~~~---:::::::---~~~~~~~~~~-------:::::::................·········....:::----------~~~~~======~~~----------~~~~~~-----------------::::::------------~~~~== ~=========~~~~----~~~~~===+++++================+++++^+++++=++++++++===================~~~~~------::---~~======~~~~----::::.................············......:::::----~~~~~~~~=======~~~~~~~~~~~~~~~~~~~---------------::::::::-----------~~~=== ~~~=======~~~~-----~~~~===+++++========++++++++++++^^^++++=++++++++++++++++===========~~~~~~~~--------~~=======~~~----::..................·············.......:::::---~~~~~~~=========~~~~~~~~~~~~~~~~~~~~~-----------::::.::::----------~~~~=== -~~~~~~~~~~~~------~~~====+++++=================++++^+++======+++++++++++=============~~~~~~~~~------~~~=====~~~-----:::..................···············......::::---~~~~~~=============~~~~~~~~~~~~~~~~~~~~~--------:::::::::--------~~~~===++ ---~~~~~~~~~-------~~~======++===========~~~~~~~==+++++========~~======================~~~~~~~~~~~~~~~~~~~~~~~----:::::......··············....·············...::::---~~~~================~~~~~~~~~~~~~~~~~~~~~~~-------:::::------~~~======++++ --------~~~~-------~~~~=========~~~~~~~~~~~~~~~~~==+++===~~~~~~~~~~~=======~~===++++====~~~~~~~~~~~==~~~~~~~~---:::::::...··················...··· ····...:::----~~~===============~~~~~~~~~~~~~~~~~~~~~~~~~~---------------~~~===+++++++++ ---------~~~---------~~~~~~~~~~~~---------------~~~====~~~~~~~~---~~~~~========+++++++=========~~~~~~~~~~~~~-----::::...·············· ······· ····..::::---~~~~~======~~~~~~~~~--------------~~~~~~~~~~~~-------~~~~~~~~===+++++====== ---:::--------------------~~~~----:---------------~~~~~~~~~---------~~~~~~====+++^^^++++++++++===~~~~~-----------::...··· ····· ···········...::---~~~~~~~~~~~~~~~~~~----::::::::::---~~~~~~~-~~~~~~~~~~~~~~======++++++===~~~~ ---:::----~~----------::--------::::::------:::----~~~~~~~------------~~~~===++++^^^^++++++++++==~~--------------::..·· ···· ··········...:::--~~~~~~~~~~~~~~~------:::......::::--~~~~~~---~~~~~~~~~~========+++++++==~~--- ~---------~~~------------------:::::::------------~~~~~~~~~~~~~---------~~~===+++++++++++++++++===~~~~~---------:::..··· ···· ·········..:::-----~~~~~~~~~~~~-----::::.......::::--~~~~~~~~~~~~~~~~~==========+++++++==~~--- ~~~~~~~~~~-----------------:::::::::------------~~~===========~~~~-------~~~======++++++++++++=====~~~~~------:::.....·············· ···..::-----::---~~~~~~-----:::::....::::::---~~~~~~~~~~~~~~~~~~~==========+++++==~~~~-- ======~~~~~~~------~~~~~---:::::-------~~~~~~~~~~====+++++++====~~~~-----~~~~========+++++======~~~~~~~---:::::.......················· ···..::---::::::----------::::::..::::::::----~~~~~~~~~~~~~~~~~~~~~~~~~=========~~~~---- =========~~~~~~~~~~~~~~~~-------~~~~~~~~~~~~~~~~=====+++++++++===~~~~~~~~~~~~~~========+====~~~~~~~-----::::::....········ ····················· ·····.....::......::::::::::::::::::::::::------~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~----::::: +++++++=====~~~~~~~~~~~~~~~~~~~======~~~~~~~~========+++^^^^++===========~~~~~~~~~~~======~~~~-------:::::::.....····· ·····............··········...··········................::::::::::---~~~------~~~~~~--------------~----::::....... +++^^++++=====~~~~~~~~~~~~=======++====~~~~==========++^^^^^^++===========~~~~~~~~~~~~==~~~----::::::::........····· ··...............·········..··· ·················....::::::::---~~~~--------~~~----------::-----:::....······· ^^^^^+++++==========~~~~=========+++===~~~=====++++++^^^^^^^^+++==========~~~~~~~---~~~~----::::............···· ····...........·······································...:::::----~~~~~------~~~~~~~-------:::::::::...···· ^^^^+++++++====================================+++^^^^^^^^^^^+++======~~~~~~~~~--------::::::....······.....·· ·····.······· ·······························..::----~~~~~~~~---~~~~~~~~~~~~~---:::::::....···· ^^^+++++++++++++++++=============++==========+++^^^^^^^^^^^^^+++====~~~~~~~~~------::::::........······.....·· ···· ·········· ····.....······················..::---~~~~~~~~~~~~~~~~~=====~~~--:::::::...···· ^^^+++++++++++++++++++++++++++++++++++++++++++^^^^^^^^^^^^^^^^++====~~~~~~~~~----:::::::::::::......·......··· ··········································........········· ······ ··..::----------~~~~~~=======~~~~~---::::...···· +++++++^^^^^+++++++++^^^^^^^^^^^+++++^^^^^^^^^^^^^^^^^^^^^^^^^++======~~~~~~~~--:::::::::::::::::::::...···········......·······..........···············.....::::....··· ··· ··...:::::-------~~~~======~~~~~~~~~--::...···· ++++++++^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^++=====~~~~~~~~---::::::::::::----:::::::..·········...::.............····················....::::::::...·· · ···...:::::-----~~~========~~~~~=~~~-::...···· ===+++++++^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^++===~~~~~-------::::::::::::------::::::..............:::::::......·······················....:::::::::..·· ···...:::----~~~~===++++========~~~-:::...···· ~======++++^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^+++==~~~----:::::::::::::---------::::::::::............:::::::::..················ ····....::::::::.·· ··..:::---~~~~~==++++++=====~~~~--:::...····· ~~======++++^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^++++==~~~---::::::::::::::--------:::::::::::::..........::::---::...················ ····.....:::::::.·· ··...::-----~~~~==++++=====~~~~---:::....····· ~~~======+++^^^^^^^^^++++^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^+++++++===~~------::::::::::::::::-------:::::::::::::::::::::::-----:::.................······.....::::::::::..·· ··....:::-------~~~========~~~~~~---::.....······ · ~~~~======+++^^^^^^+++===++++++++++++++^^^^^^^^^^^++++++========~~~----------::::::......::-------::::::::::::::::----------:::::....:::::::::::::::::::::::------::...···· ··.:::::::::-------~~~~~~~~~~~~~~~---::......·········· ---~~~~~===++++^^+++==~~~=======~~====++++++^^^++++=====~~~~~~~~~~~----------::::........::--------::::::::::::::----~~~~-------:::::-------------------------~~---:...···· ·· ··.::::::::::::--------~~~~~~~~~~~~~--:::.........······ ------~~~===+++++++==~~~~-------~~~~~~==============~~~~~---~~~~~~~~~~~-----::::..........::----------::::....::::----~~~~~~~~~~~~---~~~~~~~~~~~~~-----------------::...·· ··..::--:::::::::::----~~~~~===~~~~~~---::::::::::....... :::::---~~===+++++==~~---:::::::--~~~~~~~~~~~~~~~~~~~--------~~=======~~~--:::............::----~~~~~-::.......:::::---~~===========~~~~~~======~~~~~~---------------::.·· ····..::--::::::::::::--~~~~=======~~~~~---:::::--::::::::: :::::::--~~========~~---::.....::-----------~~~---------:::--~~~~=====~~~-:::............:::---~~~~~~--:.......::::---~~==++++++++===========++==~~~~~~~~------------::.· ····..:::::::::::::::::--~~~~======~~~~----::::----------:: ::....::--~~~=====~~~--:::.......::::----------------::::::---~~~~~~~~~---:::::.........:::----~~~~~~~-:::.::::----~~~~==++++++++++===============~~~~~~~~~~-------:::..· ·····..::::::..........:::---~~~~~~~~~~---:::::::----::::::: :..···..:--~~~~==~~~--:::...........::---~~~------::::::--------------::::::::::.....:::::-----~~~~~~~---:::---~~~~=====+++++++++++======================~~~---:::::...·· ·········...:::..............::::---~~~~~----:::...::::::::..... :.····..:---~~~~~~~---::.....······..:---~~~------::::::----------::::::::::::::::::::::-------~~~~==~~~~---~~~======+++++++++++++=======================~~~--:::....····· ···········.........·········.....::----------::..···...::::.....: ........:::----~~----::...·········..::-----------------------:::::........:::::::::::::------~~~========~====+++++===================~~~~==============~~---:::....···········.....······.........···········...:::------:::..·· ···.........:: ·.........:::-------:::..·· ···..::::---------------~~---:::...............:::::::::-----~~~==+++++++=++++^^^+++================~~~~~~~===++=======~~---::::...······.............·········......···········..::::::::::..·· ···.....::: ·...:::...::::-----::::..·· ··....::::-------------~~~~--::....······......:::::::::----~~~~==++++++++++^^^^^^++===============~~~---~~===++=======~~--:::::..······..............··········.....··· ····...::::::::..·· ····...::- ·.....:::::::------:::..··········...:::-----------~--------::...............:::------:----~~~=====+++++++++++^^^++++=============~~~~~~~~~====++++++==~~--::::...·····..............·························......::::::::.·· ··..:::- ......:::::--------::...............::-------------~~---::::....··....::::::::------------~~==============++++++++++++++=========~~~~~~~~~~=====++++++=~~--::::...............···············..·············...:::.....:::::..·· ··..::-- ..:::::::::---------:..............::::----------------:::.....···...:::::::::---~~~------~~===============+++++++++++++++========~~~~~~~~~~~=====+++==~~---::::..........······ ·········....·······......:::::......::::...··· ··..:::: ::::::::::::--------:::::::::::.....:::::::::::::::::::::.......··....::::::::----~~~~~~~~~================+++++++++^^^+++++++=====~~~~~~~~~~~~~~~===~~~-------:::::::....···· ·······...............:::::::.............··········.....:: -::::::::::::------------::::::::...........................................:::----~~~~============++++====+++++++^^^^^^^^^^^+++======~~~~~-------~~----------------:::...··· ·····......::::::::::::--:::....········.................. --:::::::::::------------------::::::...........................·...........:::---~~~~============+++++====+++++++^^^^^^^^^^^^++====~~~~~~--------------:::---~~~----::..··· ····......:::-------------::...········...:::::::::....... --:::::--------~~~~----------------:::::......................····....::::::::---~~~~~================+++++++++++++^^^^^^^^^^+++==~~~~-----:::::::------------------:::.·· ····.......:::::-------------::...........::::::::::::...... :::----------~~~~~~~-------~~~~~~~~---::::::::::::::..........····...::::::::---~~~~~~~===============+++^^^++++++++++^^^^^^+++==~~~--:::::::::::::::------------::::..·· ···........::::::----~~~~~~----::::::::::::::----:::::::..... ::----------~~~====~~~----~~~~~~~~~~~---:::::::::::::........·····...::::::::---~~~~~~================+++^^+++====+++++++++++===~~---::........::::::---------:::::::..·· ··.........::::::---~~~~~~~~~----::::----------------:::::::. :--------~~~~~=======~~~~~~~~~~~~~~-------:::::::::......···········....:::::---~~~~~~=====++++++++==+++++++++===============~~~~---::::.......:::-----------:::::::::..·· ······.........::::--~~~====~~~~~-------------~~~~~~~~--------:: ---~~~~~~~~~~===+++++====~~~~~~--------------::::::....···············....:::---~~~~~=====++^^^^^+++++++++==========~~~~~~~--------:::::........::-----::::::------::::..··· ···············....::--~~=======~~~~---------~~~~~~~~~~~~~~~~~~~--- --~~~~~~~~~~===++++++++===~~~~~---------------:::::....····· ·········....:::---~~~~=====++^^^^^^^++++++==========~~~~~---------::::::..........::-----::::::::::::::::..·······....·········...::--~~===+====~~~~~~--~~~~~~~~=============~~~~~ -~~~==========++++++++====~~~~~~~~~~~~~~~~----::::::...··············...::::---~~~~====+++^^^^^^^^^^++++==========~~~---------::::.............::::---::::::::::::::......·····.....·······.....:::--~~===========~~~~~~~~~====================~ -~=====+++++++=============~~~~~~~~~~~~~~~---:::::::...···········.....:::---~~~~====+++^^^^^^^^^^^^^+++==========~~----------:::......···....:::::::::::::::........................····.......::::-~~==========================++======+++++== -~~======++++==============~~~~~~~~~~~~~~~--::::.......········.......:::--~~~~=====+++^^^^^^^^^^^^^^+++=========~~~----------:::......···...........:::::::.........................····......:::::-~~==================~~=====++++++==+++++++= :--~~~~~========+++++======~~~~~~~~~~~~~---:::.........·······.......:::---~~~=====++++++++++++++++++++=========~~~~---------:::::.......····........:::::::.......::.........···········....:::::---~~========================+++++++++++++++== ::---~~~~~~~~==+++++++====~~~~~~====~~~---::............····....::::::::---~~~====++++++++===============++===~~~~~-----::::::::::::::....·······.....::::::......:::::::....···········....:::::---~~~========~~~~~~~~~~====++++++^^^^^^+++++== ..::-------~~===+++++======~~~~=====~~---::..............··...:::::::::---~~~===+++++++++===~~~~~~~~~~~======~~~------::::::::::::::::::...······.......::::.....:::::::::....·········......::::---~~~======~~~~~-----~~~~====+++++^^^^^+++++++ ...::::----~~~~===============~~~~~~~-----::...........····...:::--------~~~===++++++++++==~~---------~~~~~~~~------:::::::::::::::::::::...·········.........:::::::::::::.....····..........:::::--~~~=====~~~---------~~~~====+++++++++++++++ ....::::--~~~~~~~~~============~~------~---::::....·········..::--------~~~====++++^^++++==~-------------------::::::::::..::::::---:::::.....··········.....:::::----:::::::....................:::--~~====~~~-----------~~~~~=======+++++^^^^+ ...::::--~~~~~~~~~=========+===~~~----~~---:::::...········...::---------~~~====++++++++==~~---:::::::-------:::::::::.......:::::--::::::..................::::-------::::::::...................:::-~~~~~~~~~-----:::----~~~~~=======++++^^^^+ ::::::----~~~========++++++++++==~~~~-----::::::......······..:::::::----~~~~==========~~~~------------------::::..............::::::::::::...............::::::::-----::::::::...................:::--~~~~~~-----::::----~~~~~=====++++++++++++ ----------~~~==++++++++++^^^^^^++===~~--:::::::.......·······...::::::----~~~~~~~--~~~~---------------------::::.....·····......::::::---::...........::::::::::::::----:::::::::..::::::.........:::--~~~~----:::::-----~~~~======++++++++++++= ~------~~~~~==++++++^^^^^^^^^^^^^++==~--:::::::.....··········.....::::::---~~----------------------------::::.....········........::::::::..........::::::::::::::--------------::::-::::........::::-------:::::------~~~=======++++++++++==== ~-----~~~====+++++++^^^^^^^^^^^^^^++=~~--::::....·············...........::::---------------~~~------::::........·················........:::::::::::::::::::::::::------~~~~~~~~~~~~----::::......:::::----:::-----~~~~~~~=====++++++++++===~~~ ------~~==++++++++++^^^^^^^^^^^^^^^++=~--:::..···············......······....::-------------~~~~----:::..·············· ········...:::::::::::::..:::::::::----~~~==========~~~~---::::::....:::::::::----~~~~~~~~~====+++++++++===~~~-- ~-----~~==+++++++++^^^^^^^^^^^^^^^^^+=~~--::...··············......·······....::------::::---------:::..············ ·······...::-----::::::::::::::::-----~~~====++======~~~---::::::....::::::::::----~~~~~~~~====+++++++++===~~--- ~~~~~~~~====+++++^^^^^^^^^^^^^^^^^^^+==~~--:::......···········...·······....::::::::::::::::::::::::..···· ····· ·······...::::--------:::::::::----------~~~~~=========~~~----::::::::::::::::::::--------~~~~~=====++++++++==~~~--- ~~~~~~~~=====++^^^^^^^^^^^^^^^^^^^^+++==~~----:::::.....·······...·······...:::::::::::::::::...:::::..·· ···.......:::-------------:::------~~~~~~~~~~~~~~~====~~~~~~---::::::::::------:::::-----------~~~~====++++++++==~~---- =~~~~~=======+++^^^^^^^^^^^^^^^^^^^+++==~~~~---:::::::..............····....:::::::::::::::::...::::...·· ··.......::--~~~~~~~~~~----------~~~=======~~~~~~~===~~~~~~~----::::::::-------::::------------~~~~~=====+++++===~~---- =============+++++++++^^^^^^^^^^^^^+++==~~~~---------::::....................:::::::::::::::::::::....··· ····......:::--~~====~~~~~--------~~~~======================~~~~~~----:::::----::::::::-----------~~~~~~~=========~~~~---- +========+++++++++++====+++^^^^^^^^+++==~~~~~----------:::::::::::::::::......:::::::::::::::::::...······ ···.......::::::--~======~~~~~------~~~~===++++====================~~~~-----::::::::::.::::-------~~~~~~~~~~~~===~~~~~~~~---- +=========================+++++++++++===~~~~~~~-----------::::::::::::::::..::::::::::::::::::::::..······ ··.......::::::--~~=======~~~~------~~~====++++===================~~~~~----------:::::::::-------~~~~~~~~~~~~~==~~~~~~~~~---- ===~~~~~~~~~~~~=====~~~~===+++++++====~~~~~~~~~~~-------------:::::::::::::::::-----------------:::...···· ···.......:::::---~~~====~~~~~~------~~~~===+++++==============~~~~~~~~----------------::::::::---~~~~~~~~~~~=========~~~~~---