:~~~~^  ^~~~^:    :~^^~^  :^^^^: .^^^^^^^^^^^^^^^^^^^^^^^::.                           ..:::^^^^::::::::::::::::.        ..::::::::::::::::::::::         ....::::::::::::::::::::.
~JJJJ7  7J?JJ~    ~????7  !????! :????????????777???77777777~^.                     .:^~!!!!!!!!!!!!!!!!!!!!!!!!.    .:^~~~!!!~~~~~~~~~~~~~~~~~~~      .:^^~~~~~~~~~~~~~^^^^^^^^^^:
~J???7  7????~    ^????7  !????~ :77777777777777777!!!!!7777777~:                 .^!!!!!!!!!!~~~~~~~~~~~~~~~~~~.   :~~~~~~~~~~~~~~~~~~~~~~~~^~~^    .^~~~~~~^^^^^^^^^^^^^^^^^^^^^:
~????   7????     ^????   ~77?7~                          ^!7777!~.              :!!!!!!~                          ^~~~~~~                         .^~^^~^:                        
~????7  7????~    ^??7?7  ~7777~ :!7!!!!!!!!!!!!!!!!!!!!~   ^!7!!7~.            :!!!!!~   ^~~~~~~~~~~~~~~~~~~~~~. .~~~~~^   ^^^~~~^^^^^^^^^^^^^^^  .^~^^~^   :^^^^^^^^^^^^^^^^^^^^:
~????7  7????~    ^??777  ~7777~ :777777777777777777777777!^  !7!!!^.          :~!!!!^  ~!!!!!!!!!!!!!!!!!~~!~~~. ^~~~~^  ^~~~~~~~~~~~~~~~~~~~~~~  :^^^^^  :~^^^^^^^^^^^^^^^^^^^^^:
~????!  !????~    ^77777  ~7777~ ^^^^^^^^^^^^^^^^^^^^^~!!!!!  ^7!!!!.          ^!!!!~  ~!!!~~^::::::::::::::::::. ^~~~~^  ~~~~~^^^^^^^^^^^^^^^^^^  :^^^^^  ^^^^^^:::::::::::::::::. 
~????!  !?7??~    ^77777  ~7777~ .::::::::::::::::::::~!!!!!  ^!!!!~.          ^!!~!~  ~~~~!~:::::::....          ^~~~~^  ~~~~~^                   :^^^^^  ^^^^^:                  
~????!  !7777~    ^77777  ~7777~ :7777777777777777!!!!!!!!!^  ~!!!!~.          :~!~~~:  ~~~~~!~~~~~~~~~~^:.       ^~~~~^  ~~~~~~~~~~~~~^^^^^^      :^^^^^  ^^^^^:                  
~7777!  !7777~    ^7777!  ~7777~ :!!!77!!!!!!!!!!!!!!!!~~^   !!!!!~:            ^~!~~~^   ^^~~~~~~~~~~~~~~~^.     ^~~~~^  ^^^^^^^^^^^^^^^^^^^      :^^^^:  :^^^^:                  
^7777!  !7777~    ^7777!  ~777!~ :!!!!!^                   ~!!!!!~.              :~~~~~~^             ^^~~~~~^.   ^~~~~:                           :^^^^:  :^^^^:                  
^7777!  !7777~    ^7777!  ~7!!!~ :!!!!!  ^~~~~~~~~:  ~~~~!!!!!~~:.                .^~~~~~~~~^^^^^^^^:    ^~~~~^.  ^~^^^:  ^^^^^^:::::::::::^:      :^^^^:  :^^^^:                  
^7777!  !7777^    ^777!!  ~!!!!~ :!!!!!  ~!!!!!!!!!^  !!!!~~~^..                    .:^~~~~~~~~~~~~~~~^   ^^~^~^  ^^^^^:  ^^^^^^^^^^^^^^^^^^^      :^^^^:  :^^^^:                  
^7777!  !7777^    ^!77!!  ~!!!!~ :!!!!!  ^!!!!!~!!!!^  ~!~!~:                          ...::::::::^~~^~~  :~~^^^. ^^^^^:  ^^^^^^                   :^^^^:  ::^^^:                  
^7777!  ~77!7!^:::~!!!!!  ~!!!!~ :!!!!!  ^!!!!~:^!!~!^  ~!~~~.                 ...................:^^^^^  .^^^^^. ^^^^^:  ^^^^^:.................  :^^^^:  ::::^:..................
^7777!  ^77!!!!77!!!!!!~  ~!!!!^ :~!!!!  ^!~!!^..^~~~~^  ~~~~~.                :~~~~~~~~~~~~~~~~~~~~^^^^  :^^^^^. :^^^^:  ^^^^^^^^^^^^^^^^^^^^^^^  .::^::  ::::::::::::::::::::::::
 !77!!~  ^~!!!!!!!!!!~^  ^!!!!~: :~!!!~  ^!~~!^. .^~~~~^  ~~~~~:               :~~~~~~~~~~~^^^^^^^^^^    :^^^^^.  .^^^^^:    ^^^^^^^^^^^^^^^^^^^^  .::::::  .:::::::::::::::::::::.
 ^!!!!!!^              :~!!~!!^  :~!~!~  ^~~~~^.  .^~~~~^  ^~~~~:     .......                         :^^^^^^.    :^^^^^:........................  .::::::.                        
  :!!!!!!!!~~~~~~~~~~~!!!!!!~^   :~~~~~  ^~~~~^.    :~~~~^  ^~~~~:    ^~~~~~:  :^^^^^^^^^^^::::::::^^^^^^^^^:.     .:^^^^^^^:::::::::::::::::::::    .::::::::::...................
    :~!!!!!!!!!!!!!!!!!!!~~:     :~~~~~  ^~~~~^.     :~~~~^  ^~~~~:   ^~~~~~:  :~~~~~^^^^^^^^^^^^^^^^^^^^:..         .::^^^^^^^^^^^^^^:::::::::::     ..:::::::::::::::::::::::::::
       .:^^^^^^^^^^^^^::.        .^^^^^  :^^^^:.      :^^^^:  :^^^^.  ::::^^.  .::::::::::::::::::::::...               ....:::::::::::::::::::::        ..........................