~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssszzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssszzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~ss~~~s~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~zzzss~~sszs~szzzss~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszs~szzzzzzzsszzzssszzzzss~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzssssssszzzzzzzzzzzsszzzzzzss~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssszzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssssss~~~~~~~~sszzsssszzzzzzzzzzzzzss~szzzzzs~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~zzzszzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzsszsszs~~~ssszssssssssszzzzzzzzzzzzss~~~szzzzs~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzss~~~~~~sszs~~~~~~~~~~~~~~~~szzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssszzzzzzzss~~~szzzzzzzzssszzzzzzzzzzzzzss~~~~~ssss~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~szs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzss~~~~szzzz~~~~~~~~~~~~~~~szzzzzzzzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~~~~~~~~~~~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzss~s~zzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szszzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssszzzzzzzss~~szzzzz~~~~~~~~~~~~~~~szzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzs~~~~~~~~~zzzzzs~~~~szs~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~~~~~~~~~~~~szzsssssssssszzzzzzzzzzzzzzzzzzzzzszzsss~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~sssszzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzzzzs~~szzzs~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzz~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzs~~~~~~~~~zzzzzzs~~szzs~~~~~~~~~~~~~~~~~~~~~~~sszzzss~~~~~~~~~~~~~~~~~~~ssssssssssszzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszss~~~~~~~~~~~~~~~~~~~~~ssss~~~~~~~~ssssssss~~~~~~~~~~~~~~~~~~~~~~~szzsszssszzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzs~~szzss~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzz~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssszzzzzss~~~~~~zzzzzzzs~~zzzs~~~~~~~~~~~~~~~~~~~~~sszzzzzzss~~~~~~~~~~~~~~~~~~~sssssszsszzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzs~~~~~~~~~~~~~~~~~~~~sszzzsss~~~~sszzzzzzzzssss~~~~~~~~~~~~~~~~~~zzzzzzzszzzzzzzzz~~~~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~zzzszzzzzzzs~~~s~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzs~~s~~~~~szs~~szzss~~~~~~~~~~~~~szs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~ss~~~~~~~~~sszzzzzzzzsss~~~~~szzzzzs~~~ss~~~~~~~~~sss~~~~~~~~sszzzzzzzzszs~~~~~~~~~~~~~~~~~sssszzzzszzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~zzzzzzsssss~~~~~~~~~~~~~~sssszzzzss~ssszzzzzzzzzzzzss~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzss~~sszs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~zzzssszzzzzzs~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzssss~~~sssszzzzz~~~~~~~~~~~~szzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szsszzs~~~~~~~~szzzzzzzzzzzss~~~~szzzzs~~~~~~~~~~~~~~sszssssssssszzzzzzzzzzzzzss~~~~~~~~~~~~szssszzzzzzzzzzzzzzzzzzzzzzzzzzzz~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~zzzzzzzsszzs~~~~~~~~~~~~sszzzzzzzzzzssszzzzzzzzzzzzzss~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzsssssszzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~zsssszzzzzzs~~~~~~~~~~~~~~~ss~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~sszzzzzs~~~~~~~~~~~sszzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssszzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~~~~~~~~~~szzzzzss~~~~~~~sszzzzzzzzzzzzs~~~~sszzs~~~~~~~~~~~~~sszzzzzsssssszzzzzzzzzzzzzzssss~~~~~~sssszzsssszzzzzzzzzzzzzzzzzzzzzzsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssszs~~~~~~~~~~~~~~~~~~~~~~~szzzzzsszzzss~~~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~sszzzzzzzzzsssssszzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssszzzzzzs~~~~~~~~~~~~~~~szssssszzzzzzzzzzzzzzzzzzzzzzzzzzzzs~sssszzzzs~~~~~~~~~~szzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzzss~~~~~~~~~~~~~~~~~~~~~~~~~sszss~~~~~~~~~~~~~~~~ssszzzzzs~~~~~~sszzzzzzzzzzzzzss~~~~sss~~~~~~~~~~~~sssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzssssssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~~szszzzzzs~~~~~~s~~~~~ssss~~~~~~sszzzsszzzzzzz~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~~~szszzzzzzss~~sszzzzss~~~~~~~~~~~~~~~~~~~~~~~sss~s~~ssszzzzzzzs~~~~~~~~~~~~~~szzzzzszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzssssssssss~~~~~~~~~~sszzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssszs~~~~~~~~~~~~~~~~~~~~~~~~~zszzzss~~~~~~~~~~~~~~~zzzzzzzzs~~~~~sszzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~sssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzsssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzssszzzzzzzzs~~s~~szss~sszzzzs~~~~~~sszsszzzzzzzzzss~~~ssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzsss~~~~~~~~~~~~~ss~~zzss~~~~~~sszss~~~~~~~~~~~~~~~~~~~~~~szzszzs~~~szzzzzzzs~~~~~~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzsssssss~~~~~~~~~~~~~szzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzs~~~~~~~~~~~~~~~szzzssss~~~~sszzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~sssssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrrzzzzzzzzzzzzzzzzzzzzzzzhzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzszzzzzzzzsssszssszzsszzzzzzzs~~~~~~ssssszzzzzzzzzzsssssssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~~~~~~~~~~~~~~~~~~~sszzzzzzzzssszzzzzzzzs~~~~~~~~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzsssssss~~~~~~~~~~szzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~zzzzzzs~s~~~~~~~~~~~~~sss~~~~~~sszzzzzzzzzzzzzzzzzzzzzs~~~~~~~~ss~~~ssssssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~zzzzzszzzzzzzssszzzzzsssszzzzzzzs~~~~~~~~ssssszzzzzzzzzzzzsssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~ssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzsss~~~~~~sszzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzzsszs~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzss~~~~~~~szzs~~ssrrszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzhhhzzzzzzhzzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzsszzzzzzssszzzzzzzzzzzzzzzzzs~~~~~~~sszzzzzzzzzzzzzzzzzzszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzsss~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~sssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzss~~~~~szzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszssssss~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzs~~~~~~~szzss~ssszzrrzzzzzzzzzzzzzzzzzzzzzzzzzzzrrrrrzzzzzzzzzzzzzzzzzzzhhhhhzzzhhzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssszzzzzzsssszzzzzzzzzzzzzzzzzs~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~s~~~~~~~ssssszzs~~~~~~~~~~~~~~~~~sszzzzzzzzzzzzzzzzzzzsszzs~~~~~~~~~~~~~~~~~~~~~ssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~ssszzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~zsssssssssss~~~~~~~~~~~~~~~~~zzszzzzzzzzzzzzzzzzzzzs~~~~~~~szzzsssszzzzzzrrzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzhhhhzzhhhzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzssszzzzzzzzzzzzzzzzzs~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz~~~~~~~szzss~~~szzzzzzzzss~~~ss~~~~~~~~sszzzzzzzzzzzzzzzzzzzzs~~szs~~~~~~~~~~~ss~~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzssssszzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszsszzsssssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzsssszzzzss~~~~~~~~~~~~~~~~~ssssszzzzzzzzzzzzzzsss~~~~~~~sszzssszzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzrrzzzzzzzzzzzzzzzzzzzzzzzzzhhhhhzzhhzzzzzsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzsszzzzzzzzzzzzzzzsss~~~~~~~~~sssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~szzzzzssszzzzzzzzzzzssszzsss~~~ssszzzzzzzzzzzzzzzzzzzzzs~~szzs~~~~~~~~~szz~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzszzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzsszzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzsszzzzzzzs~~~~~~sss~~~~~~~~~~~sszzzzzzzzzzszss~~~~~~~~~~ssssszzzzzzzzzzrzzzzzzzzzzzzzzzzzzzrrzzzzzzzzzzzzzzzzzzzzzzzzzzhhhhhhhzzzzzzzsszzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszs~~szzzzzzzzzzzzzss~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~szzzzzzzzzzzzzzzzzzzzzzzzzssssszzzzzzzzzzzzzzzzzzzzzzzzs~~~ss~~~~~~~~~~szzzs~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzszzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzssszzzzzzzzs~ss~szzss~~~~~~~~~~~szzzzzzzzssszs~~~~~~~~~~~~ssszzzzzzzzzzrzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhzzhhhzzzzzzzszzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssszzzzzzzzzz~~~~~~~~~~~~~zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrs~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~szzzzs~~~~~~~~zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssssszzzzzzzsssszzzzzzss~~~~~~~~~~~~szzzzzzssss~~~~~~~~~~~~~sszzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhhhzzzzzzzzzzs~~~~~~~~~~~zzzz~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzz~~~~~~~~~~~~ssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzsszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz~~~~~~~~~~~~~~~~szzzzzs~~~~~~~~~zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssszzzzzzzzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssszzzzzzzzzsszzzzzzzzsssss~~~~~~~~~sszzzzzs~~~~~~~~~~~~~~~szzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhhhhzzzzzzzzzs~~~~~~~~~~~~zzzz~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssszzzss~~~~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz~~~~~~~~~~~~~~~szzzzzzzs~~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzszzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~zzzzzzzzzzssssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzzzzzzsszzzzzzzzzzzssss~~~~~~~sssssss~~~~~~~~~~~~~~szzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhhhhzzzzzzzzss~~~~~~~~~~~szzzz~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szss~~~~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrrrrzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~ssszzzzzzzss~~~~~~~~~ssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzsszzzzzzzzzzzzzzzzzzss~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~zzzzzzzzzzssszzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzrzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhzzzzzzzzss~~~~~~~~~~~~szzzzzs~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrrzzzzrrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~szzzzzzzzzzzz~~~~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzsssssszzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~zzzszzzzsszzzzsss~~~~~~~~~~~~~~~~~~~ss~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzzzzzzzrzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~szzzzzzs~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^zzzzzs~~~~~~~~~~~~~~szzzzzzzzzzzs~~~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~ssszzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzsszzzss~~~~~~~~~~~~~~~~~~~~sszs~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzzzzzzzzzrrzzzzzzzzzzzzzrzzzzzzzzzzzzzhhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~sszzzzzzss~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszsszzzzzzzhhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^zzzzss~~~~~~~~~~~~~~~zzzzzzzzzzzss~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~sszzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~zzzsssszzsss~~~~~~~~~~~~~ssssssszzs~~~~~~~~~ssszzzzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~ssszzzzzzzzzzzzzzzzzrzzzzzzzzzzzzrzzzzzzzzzzzhhhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~sszzzzzzzzzs~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssszzzsszzszzhhhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^^zzzzzzs~~~~~ss~~~~~~~~~sszzzzzzzzzs~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzssss~~~~~~~ssszzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~~~~~~~~~~~~szz~~~sszzs~~~~~~~~~~~~~ssszzzzzzss~~~~~s~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzsss~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzrzzzzzzzzzzzhhhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~sszzzzzzzzzzzss~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzsszzzzsssszzzhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^^^^zzzzzzzss~~~szzs~~~~~~~~~~sszzzzzzs~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~sszzzzzzzzzzzzzz~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzz~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~~~~sszzzzzzzzzzs~~~szss~~~~~~szzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzrrzzhzzzzzzzhhhzzzzhzzzzzzzzzzzzzzzzzzzzzzzzzzzzsss~~~~~~~~szzzzzzzzzzzzzs~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szss~sszs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssszzzzzzzzzzzszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^!^^zzzzzzzss~~~sszzzsss~~~~~~~~ssszzss~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~szzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssszzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzzzzs~~~szzzzs~~~~~~~szzzzzzzzzzzzzsszzzzzzs~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzrzzzzzqzzrzzzzhhzzzzzzzzzzzhhhzzzzhhzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~zzzzzzzzzzzzzzs~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzssszzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzhhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^!^^zzzzzzzzs~~~~szzzzsszs~~~~~~~~~~szs~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~sszzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssszzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~ssszsszzzzzs~~~~zzzzzz~~~~~~~~szzzzzzzzzsss~~ssszzs~~~~~~~~~~~~~~~~~~~~~s~sszzzzzzzzzzzzzzzzzzzzzzzzrzzzqlqqrzzzhhhhzhhhzzzzzhhhhzzhhhzzzzzzzzzzzzzzzzzzsszzzzzs~~~~~~~~zzzzzzzzzzzzzzzs~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzssszzzs~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzhhhhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^^^zzzzzzzzs~~~~~~sssssszs~~~~~~~~~~~ss~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~sszzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzz~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~ssssszzzzzs~~~~~~szzss~~~~~~~~~~~zzzzzsss~~~~~~~ss~~~~~~~~~~~~~~s~~~~~~ssszzzzzzzzzzzzzzzzzzzzzzzzzzzrzqlllllqzhhhhhhhhzzzzzzzhhhhzhhhzzzzzzzzzzzzzzzzzzzszzzzzss~~~~~~sszzzzzzzzzzzzzzz~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~ss~~~~~~szsszzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~zzzzzzzzzzzzzzzzhhhhhhhzzzzzzzzzszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^zzzzzzzzzzs~~~~~~~~ssszzzzzs~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~szzzzzzzzzzzzsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szsssssszzzzzzzsss~~~~~~sss~~~~~~~~~~~~~sss~~~~~~~~~~~~~~~~~~~~~~~ssszzssssssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzrqlllllllhhhhhhhhhhzzzzzhhhhhhhhzzzzzzzzzzzzzzzzzzzsssszzss~~~~~~~~szzzzzzzzzzzzzzzz~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~sszzs~~~~sssssszzss~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzhhhhhhhzzzzzzzssssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^zzzzzzzzzzzs~~~~~~~~~~~szzzzzzss~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~szzzsszzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~zzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzszzzzzzzzzzzsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssszzzzzzsszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzqllllllllhhhhhhhhhhzzzzzhhhhhhhhzzzzzzzzzzzzzzzzzzzss~~szss~~~~~~~~~~zzzzzzzzzzzzzzzzs~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~szzzzzs~~~zzzsssssss~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzhhhhhzzzhzzzzzzssssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^^^^^^^zzzzzzszzs~~~~~~~~~~~szzzzzzzzs~~~~~~~~~~~~~~~~~~~~sszzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~sssszzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~zzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~sszzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssszzssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzqlllllllllhhhhhhhhzzzzzzzhhhhhhhhzzzzzzzzzzzzzzzzzzzs~~~ss~~~~~~~~~~~szzzzzzzzzzzzzzs~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~szzhhhzs~~zzzzzsssszzs~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzhhhzzzzzzzzzzzzzssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^^^^^^^^^^^zzzzzssss~~~~~~~~~~~~sszzzzzzzs~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~szzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssszzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~szzssszzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzqllllllllqzhhhhzzzzzzzhzhhhhhhhhhzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~sszzzzzzzzzzzzs~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~szzhhhzzsszzzzzzssszzzzss~~~~~~~~~~~~~~~~~~sszzzzzzzzzzzzzzzzzhhhzzzzzzzzzzzzzsszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^^^^zzzzz^^^^^^^!!!!^^^zzzzss~~~~~~~~~~~~~~~~szssssss~~~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzzzzzzzzz~~~~~~~~~~~~~~~~~~szss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~~sss~~sssszssssszzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhhhllllrzzhhhhzzzzzzhhhhhhhhhhhzzzzzzzzzzzzzzzzzzzzz~~~~~~~~~~~~~~~szzzzzzzzzzzzzs~~~~~~~~~~~
~~~~~~~~~~~~~~~~~szzhhhzzsszzzhhzssszhzzzzs~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzssszzzzzzzzzzzzzzzzzzzzzzzz^^^^^^^zzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzz^^^zzz^^^^^^^^zz^^^!!!!!!^^^^^zzzss~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzz~~~~~~~~szzzssszzzzzzzzsszzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~~~~~sssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzhhzzhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhhhllqzrzzhzzzzhzzzzhhhhhhhhhhzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~szzzzzzzzzzzss~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~zzzzzzzsszzzhhzzzsshhhzzzzs~~~~~~~~~~~~~~~~zzzzzzzhzzzzzzzzzzzzzzzzzzzsssszzzs~szzzzzzzzzzzzzzzzzzzzzzz^^^^^!!^^^zzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzz^^^^zzz^^^^!^^^^zz^^^^!^^^^^^^zzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~zzzzzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~~~~~~~~~szzzzzs~~~~ssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzzhhhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhhhhlhhzzrzzzzzzhhhzzzhhhhhhhhhzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~~~szzzzzzzzzzzs~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~szzhzzs~szzhhhzzsszhhhzzzzs~~~~~~~~~~~~~~zzzzzzzzhzzzzzzhhhzzzzzzzzzss~~~szzs~s~szzzzzzzzzzzzzzzzzzzzzzzz^^^^!^^^zzzzzzzzzzrzzzzzzzzzzzzzzzzz^^^^z^^^zzz^^^!!^^^^^^zz^^^^^^^^zzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szz~~~~~~~~sszzzzzzs~~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzssss~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzhhhzzhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhhhhhhhhzzrzzzzzhhhhhzzzzzhhhhhzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~szzzzzzzzzzss~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~szzzs~szzzhhhzzssszzzzszs~~~~~~~~~~~~~~zzzzzzzzhhhzzzzzhhhhhzzzzzzss~~~~~ss~~~~~szzzzzzzzzzzzzzzzzzzzzzzzz^^^^^zzz^^^^zzzzrzzzzzzzzzzzzzzz^^^^^^zzzzzz^^^!!^^^^zzzzzzz^^^zzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzs~~s~~~sszzzzzzzs~~~szzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzsssszss~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzhhhhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhhhhhhhzrzzzzzhhhhzzzzzzzhhhhzzzzzzzzzzzzzzzzzzzzz~~~~~~~~~~~~~~~~~sszzzzzzzzzs~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~sssszzzzhhhhzzzs~sszs~s~~~~~~~~~~~~~~sszzzzzzhhhhhhhhzzzhhzzzzzzzzs~~~~~~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzz^zzzz^^^^^^zzzrzzz^^^^zzzzzz^^^^zzzzz^^^^^^!!^^^^zzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssszsszzzzzzzzzss~~szzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzsszzss~~~~~~~~~~~~~~~~~~~~~~~~zzzzzzzzzhhhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhhhhhhhhzrzzzzzhhzzzzzzzzzhhzzzzhzzzzzzzzzzzzzssss~~~~~~~~~~~~~~~~~szzzzzzzzzzs~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~zzzzzzzhhhhhzzzs~~~s~~~~~~~~~~~~~~~~~ssszzzzzzhzhhhhhhhzzzzzzzzsss~~~~~~~~~~~~~~~ssszzzzzzzzzssszzzzzsssssszzz^^^^^^^^^zzzzrz^^^^^^zzzzzz^^zzz^^^^^^^^^!!^^^zzzzsssszzzzzzzsssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzzzzzzs~~~szzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~ssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzszs~~~~~~~~~~~~~~~~~~~~~~~zzzzhhhhzzhhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhhhhhzzrzzzzzzzzzzzzzzzzhhhzzzzzzzzzzzzzzzsss~~~~~~~~~~~~~~~~~~~~~zzzzzzzzzzs~~~~~~~~~~~~~~
~~~~~~~~~~~~ss~szzzzzzzhhzzhhzzzz~~~~~~~~~~~~~~~~~~~~~~ssszzzzzzzzzzhhhhhhzzzzzszs~~~~~~~~~~~~~~~~~~~~ssszzzssss~~~sszzzs~~~~sszzz^^^!!^^^^zzzrzz^^^^^^^^^zzzzz^^^^^^^^!^!!!^^zzzzzs~~~~szzsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzssssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~ssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~zsszzhhhhhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhhhhhzzrzzzzzzzzzzzzzzzzzzhhzzzzzzzzzzzzzzzss~~~~~~~~~~~~~ssss~~~~~sszzzzzzzzs~~~~~~~~~~~~~~
~~~~~~~~~~~szzszzzzzzzzzzzzzhzzzss~~~~~~~~~~~~~~~~~~~~szzzzzzzzsszzzzzhhzzzzzsszz~~~~~~~~~~~~~~~~~~~~~~ssszzs~~~~~~~ss~~~~~~~~szzzz^^!!!^^^^^^^r^^^!!^^^^^^^^^^^^^!!^^!!!!!^^zzzszzs~~~~~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzssssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~sssszzzzzzzzhhhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhhhzhzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~szzzzs~~~~~ssszzzzzs~~~~~~~~~~~~~~~
~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~szzzzzzzzsszzzzzzzzzzzzsss~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~sszz^^^^!!!!^^^^^^^^^!!!!!^^^^^^!!^^!!!!!!!^!^^^zzzsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzssssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~ssssssszzzzzzzzzzhhhhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~sszzzzss~~~~~sszzzzzs~~~~~~~~~~~~~~~
~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~sszzzzzzsszzzzzzzzzzzsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzz^^^^!!^!!^^^^^^^^^!!!!!^^^^!!!!!!^^!!^^^^^^^zss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzssssssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~szzzzzzzzzzzzzzzzhhhhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~szzzzzzzs~~~~~ssszzzs~~~~~~~~~~~~~~~~
~~~~~~~~~szzzzzzzzzzzzzzzzzzhzzzzs~~~~~~~~~~~~~~~~~~~szzzzzzzsszzssssssszzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~zzzzzz^^^^!^^^^^^^!!^^^!!!^^!!!!^!!!!!^^^^^^^^^^^^zzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssssssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzr~szzzzzzzzzzzzzzzzzzhhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~szzzzzzzs~~~~~~~szzs~~~~~~~~~~~~~~~~~
~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~szzzzzssssssss~~~szzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szz^^^^^^^^^^^^^^^^^^^^^^^^^^^!!!!!!^!!^^^z^^^^^z^zzs~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~sszzzzzzzzzzzzzzhhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrrzzzzzzzzzzzzzzzzzzzzhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~szzzzzzzzss~~~~~~~ss~~~~~~~~~~~~~~~~~~
~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~sssssss~~sszs~~~~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szz^^^^^!^^^^^^^zzz^^^^^^^^^^^^^!!!!^!!^^^zzz^^zzzzzss~~~~~~~~~~~~~~~~~~~~~~~~sszzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~zsszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~szzzzzzzzzzzzzzhhhhzzhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~szzzzzzzzzs~~~~~~~~s~~~~~~~~~~~~~~~~~~
~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~sz^^^!!!^!^^zzzzzzzzzz^^^^z^^^^^^!^^!!^^^zzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~sszzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~szzzzzzzzzzzzzhhhhhzhhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz~~~~~~~~~~~~~szzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzz~~~~~~~szz^^^^^^^^^zzzzzzzzzzzzzzzzzz^z^^^^^^^^^zzzzzzsszzzs~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzsss~~~~~~~~~~szzzzzzzzzzzzzzhhhhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~sszzzzzzz~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzz~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~szzzzzs~~~~~~sszzzzz^^^^zzzzzzzzzzzzzzzzzzzzzz^^^^^^zzzzzsss~~~sss~~~~~~~~~ss~~~~~~~~~~sszzzzzzzzzzzsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~szzzzzzzzzzzzzzzhhhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~sszzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~ssszzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszss~~~~~~~szs~~~~~~~~~~~~~~~~~~~~~~~sszzs~~~~~~~zzzszzz^^^zzzzzzzzzzzzzzzzzzzzzzzz^^^zzzzzzs~~~~~~~~~~~~~~~~sszzss~~~~~~ssszzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~szzzzzzzzzzzzzzzhhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~szzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~~szzzzs~~~~~~~zzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssszz^^zzzzzsssssssszzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~sszzzzzssssssszzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzsszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~ssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzhhhzzzzzzzzzss~~~~~~~~~~~~~~szzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~szzsssszzzs~~~~~~~szzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzss~~~~~~~sssssszzzzzzzzzzzzss~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~szzzzzzzzzzzzzzzzzzzzzzzzzzzzzzszzzzzzzs~~~~~~~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzhhhhhzzzzzzsss~~~~~~~~~~~~~~~~zzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~zzzzzzzssszss~~~~~~~zzzzzszs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~zzssss~~~~~~~~~~~~~~szzzzzzzzzzzzs~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~~~~szzzzzz~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzzzzssszzzzss~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzhzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzhhhzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~zzzzzzzzsssss~~~~~~szzzzzzzz~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~szzssssssszzs~~~~~~~~~~~~~~~~~ssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~szzz~~~~zzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzzsss~sssss~~~~~~~~~~~~~~~~~~zzzzzzzzzzzhzzzzzhhhzhhzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzhhzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~szzzzhzzzzsssssss~~~~zzzzzzzz~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~ss~~~~~~~~~~~~~~~~~~~~~~~~~sssssszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssszzss~sszzz~~~~szzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzsssszzzzzssss~~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzzzzzzzzzzhhhhhhhhzzzzzzzzzzzzzzzzzzzzzzzrrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzssss~~~~~~~~~~~~~~~~~~~~~~szzzzzhhhzzss~zzzzs~~~szzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssssszzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzssszzzz~~~~~ssszzzzz~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzsss~~~ss~~ssssss~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzzzzzzzzzzhhhhhhhhzzzhzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzhhzhzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~szzzzzzzzzzzzzzzzzzsssszss~~~~~~~~~~~~~~~~~~~~zzzzzhhhhhzzzzzzzzss~~~szzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzsssszzzzzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzszzzzs~~~~~~~~sssszs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszz^zzzzzzzzzzzzzzzzhhhhhzzzhhhzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzhhhhhzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzsszzzs~~~~~~~~~~~~~~~~~~~zzzzzzzzhhhzzhzzzzzzss~~~~zzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzsss~~~~~~~~~~~~~~~~~~~~~~~~~~ssszzzssszzszzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzzzzzzzzs~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzz^^zzzzzzzzzzzzzzzzzhhzzzhhhhhzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzhhhhhhzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzsszzzzs~~~~~~~~~~~~~~~~~sszzzzzzzzzzzhhzzzzzzzs~~~~sss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzszs~~~~~~~~~~~~~~~~~~~~~~~~szsszzzzssssszzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~szzzzzzzzzzzzzzz~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssz^^^zzzzzzzzzzzzzzzzzhhzzhhhhzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzhhhzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzszzzzzs~~~~~~~~~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzs~~~sszzzzzzzzzzssszzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzss~~sszzzzzzz^zzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szz^^^zzzzzzzzzzzzzzzzzzhzzhhhzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzhhhhhzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~szzzzzzzzzzzzzzzzzzzsszzzzzs~~~ssssss~~~~~~~~~zzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~sszzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~szzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzz~~~~sszzzzzzzzs~~~sssssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzsszzzzzzzz^^zzzzsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~zz^^^zzzzzzzzzzzzzzzzzzzzzzzhzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzhhhhhzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~szzzzzzzzzzzzzzzzzzszzzzzs~~~szzzzzzs~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzss~~~~szzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzs~sszsszzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzss~~~~~~~szzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzz^^^zzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~z^^^^zzzzzzzzzzzzzzzzzzzzzzzhzzhhzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzhhhhhzzzss~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~szzzzzzzzzzzzzzzzzzsszzss~~~szzzzzzzzs~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzzzz~~~~szzzsszzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzsssssssszzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~ssszs~~~~~~~~szzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzz^^zzzzzzzz^^^^^^zzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssszzzsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssszz^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzhhhzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzhzzzzzss~~~~~~~~~~~~~~~sss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~szzzzzzzzzzzzzzzzzzssss~~~~~~szzzzzzs~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzz~~~~szzsszzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzssssssssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~~~~~~~~~~ssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszz^^^zzzzzz^^^^^^^^^zzzzs~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssss~~~~~^~sssz^z^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzhhzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~~s^^s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~szsssszzzzzzzzzzzzzss~~~~~~~sszzzzs~~~~~~~~~~~~~zzzzzzzzzzzzzzzzzzzzzzzzs~~~~sssszzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzssssszs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssszz^^^^zzzz^^^^!!^!^^^zzzzs~~~~szzss~~~~~~~~~~~~~~~~~~~~~~ssszzzzzzzzzzzzzss~~~~~~~sss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzzzzs~~~^^~szz^^zz^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~s^^ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~s~~ssszzzzzzzzzzzzzs~~~~~~~~szzzs~~~~~~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzs~~~~~~szzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssszzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzz^^^^^^^^zz^^!!!^!!^^^zzzss~szzzzzzsss~~~~~~~~~~~~~~~~~ssszzzzzzzzzzzzzzzzzsss~ssszzzsssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssszzzzzzzss~~^^^^szz^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~s^^^ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~szsszzzzzzzzzzzzs~~~~~~~~~szs~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~szzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzz^^^^^^^^^^^^^^!!!!!!^^^zzzsszzzzzzzzzsss~~~~sss~~~~sssszzzzzzzzzzzzzzzzzzzzzzzsszzzzzzzzzsss~~~~~~~~~~~~~~~~~~~~~~~~sssszzzzzzzz^zzzzs~^^^^^^^^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~sss^!^ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~zzzsszzzzzzzzzhzzss~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~zzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzz^^^^!!^^^^^^^^!!^^!!!^^^zzzzzzzzzzzzzzzsssssszzss~~sszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzzzzz^^zzzs^^^^^^^^^^^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~ssss^^^ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~szzzzszzzzzzzzhhzzzs~~~~~~~~~~~~~~~~~~~~~~sszzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~sszzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssszzzzzz^^^!!!^^^^^^!!^^!^!!!!^^zzzzzzz^^zzzzzzzzszzzzzzsszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzss~~~~sssss~~~~~~~~~~~sszzzzzzzzzzzz^^^zzz^^^^^^^^^^^^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzss~~~~ss^^ss^^s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~szzzzssszzzzzzzzhhzzsss~~~~~~~~~~~~~~~~~~~~szzzzzzzzsszzzzzzzzzzzzzzzzz~~~~~~~~~zzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sszzzzzzz^^^^!!!^!^!^!^^^^^^^^^^!^^^^^zzz^^^^zzzzzzzzzzzzzzszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzssssszzzssssss~~~~ssssszzzzzzzzzzzz^^^zzz^^^^^!^^^!!!^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzsss~~~ss^^ssssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~zzzzzzsszzzzzzzzzzzzzsss~~~~~~~~~~~~~~~~~~szzzzszzzssszzzzzzzzzzzzzzzzz~~~~~~~~~~szz~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~zzzzzzzz^^^^^!!!!!!!^^^^^^^^^^^^^^^^^^^^^^^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzssszzzzzzzzsssrszzzzzzzzzzzzzzzz^^^^^^z^^^^^!!^!!!!^^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzss~~sss^^^s~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~szzzzzssszzzzzzzzzzzzzzssssss~~~~~~~~~~~~~szzzzsss~~szzzzzzzzzzzzzzzss~~~~~~~~~~~~zs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzz^^^^^^!!^!!^^^^^^z^^^^zzz^^^!!!^^^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzhzzzzz^^^^^^^^^^^^!!!!!!^^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzrrrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzz^^^zzzzzzzzzzzzzzzzss~s^^^^^s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~szzzzs~szzzzzzzzzhzzzzzzzszzss~~~~~~~~~~~~sss~~~~~~~zzzzzzzzzzzzssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~zzzzzz^^^^^!!!!!!!^^^zzzzzzzzzz^^^^^!!^^^zzzzzz^zzzz^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzhhzzzzzzzz^^^^^^^^^!!!!!!!!^^^^^zzzz^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrrzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzz^^zzz^^^^^zzzzzzzzzzzzzzzzzssss^^!^^ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~sszs~szzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzss~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szsszzzz^^^^^^!!^!^^zzzzzzzzzzzzz^^^^^^^zzzzz^^^^z^^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzhhzzzhzzzzzhzzzz^^^^^^^^^!!!!!^^^^^^^zz^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzz^^zzz^^^^^zzzzzzzzzzzzzzzzzzzzs^^!!^ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~~~~~~~~szzzzzzzzsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssszzzz^^^^^^!!!!^^zzzzzzzzzzzzzzz^^zzzzz^^^^^^z^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzhhhhzzzzzzzhhhzzzzz^^^^^^^^^!!!!^^^^^^zz^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzz^^^^zzzz^^^zzzz^^^^^^zzzzzz^zzz^^^^!^^ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzzzzzzzzzzzzss~~~~~~~~~~~~~~~~~~~szzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzz^^^^^!!^^zzzzzzzzzzzzzzzzzzz^^^^^^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzhhhhzzzzzzhhhhhhzzzzzz^^^!!^^^!!!^^^^^zz^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzz^^^^^^zzzzzzzzzz^^^^^^^^^zzz^^z^z^^!!!^^s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzztttzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~sszzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssszzzzz^^^!!^^zzzzzzzzzzzzzzzzzzzzz^^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzhhzzzzzzhhhhhhhhzzzz^^^^^!!!^!!^^^^zzzzz^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^^^z^^zzzzzrzzzz^^^^^^^^^^^zzzzzz^^^^^!!!^^^^^^^^^^^^^!^^^s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzztttttzzzzzzzzss~~~~~~~~~~~~~~~~~~~~~~s~zzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssszzzz^^!^^^zzzzzzzzzzzzzzzzzzzzzzz^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzhhhhhhhhhhhhzzz^^^^^!!!!!!^^^^^^^^zz^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzrrrrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^^^^^^^zzzzzzzrzzz^^^^^^!^^^^^^^^^^^^^^!!!^!^^^^^^^^^^^^^^^t~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~sztttttzzzzzzzttzttzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~zzzzz^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzhhhhhhzzhhhzz^^^^^^^^!!!!!^!^^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrrrrzzrrrzzzzrrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^!^^zzzzzzzzzzr^^^^^!!^!^^^^^^^^^^^^^!!^!!!^^^^!^^^^^^^^^zs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~sqttztttttzzzzttttztzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~sqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzz^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhhhzzzzzzzrzzzzzhhhhhhhzzzzzzzz^^^^^!!!!!!!!!^^^^^zzzqzqqzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzrrzzzzzzzzzrrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^^^^^zzzzzzzzzzzz^^^^!!!!!^^^!!!^^^^!!^!!!^^!!^^!!^^^^z^^z^zs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~sqttttttttzzztttttttzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqsqtqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzz^^^zzzzzzzzzzzzzzztzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhhhhzzzzzzzrzzzzzzhhhhzzzzzzzzzz^^^^^^^^!!!^!^^^^^^zzqlqllqzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzrrzzzzzzzzzzzzzzzzzzzzzzzzzz^^^^^^^^zzzzzzzzzzz^^r^^!!!!!^!!^!!!!!^^!!!!^^^^^^^^^!^^^zzz^^zzz~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~sqttttttttttttttttttzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqttttqttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzz^^^zzzzzzzzzzzzzzztttzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhhzzzzrrzzzhhzzzzzzzzzzzzztt^^^^^!!!!!^^^^^zzzqllllllqzzzzz^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzz^^^^^^^^^zzzzzzzzz^^^^r^^!!!!!!!!!!^!!^^^^!^^^^^^^^^^^^^^^zzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~sqttttttttttttttttttttzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqttttttttq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzz^^zzzzzzzzzztttzztttttzzzzzzzzzzzzzzzztzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhhhhzzzzzzrzzzzzzzzzzzzzzztttt^^^^^!!!^!^^^^zzzzqllllllqzzzz^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzrrrzzzzz^^^!!!^^zzzzzzzzz^^^^^^^r^!^^^!!!!!!!!^^^^!^^^^^zzz^^^^^^^zzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~sqttttttttttttttttttttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqqttt^^ttttq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzzzzzzztzztttttttttztzzzzzzzztzzzztttzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhhhhzzzzzzzzrzzzzzzzzzzzzzttttttt^^^^!!^^^^^^zzzzzqllllllqzz^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzrrrrrzzzzzzzzrzzzrrzz^^^^!!!^^^^^^^^zz^^^^^^^^^^^!^^^!^^^^^^^^^^^^^^^zzzzzz^^zzzzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~sqttttttttttttttttttttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqtttttt^^^ttq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzztzzzzttttttttttttttztzzzzzttttttzztttzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzhhhzzzzzzzzzzrztttttzzzzzzttztttt^^^^^^^^!^^^^^^zzzqlllllqzz^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzrrrrrrrrzzzzzzrz^^^^^!^^^^^^^^zzz^^^^^!^^^^!!^^^!^^^^^^^^^^^^^^zzzzzzz^^zzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~sqttttqqqqtttttttttttttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqttttt^^^ttqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzttzzzztttttztttttttttzzttttttttttttztzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzttzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrttttttzzzztttttttttt^^^^^^!!^^!^^^zzzqqllqzz^^!!^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzz^^^^^^^^^^^^z^^^^^^!!^^^^!^^^^^^^^^^zzzzz^^^^zzzzzzzz^zzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~sqttqqssssqqqttttttttttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqqttt^^^^^^^ttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szzzzzzzzztttttttttttttttttttttttttttttttttttzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzttzzzzzzzzzzzzzzzzzzzzzzzzztttttttrrrttttttttttzztttttttt^^!!!^!!^^^z^^zzqqz^^^^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrrzzz^^^^!^^!!^^^^^^^^!!!!!^^^^^^^^^^ttttzzzzzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~sqqss~~~ssssqqqttttttttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqtttt^^^^^^ttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~zzzzzzzzztttttttztttttttttttttttttttttttttttttzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzztttztttzzzzzzzzzzzzzzzzzztzttttttttttrrrtttttzzzzttztttttt^^!!!!^^^zz^^^^^zzz^^z^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^zzz^^^^zzzzzzrrzzz^^^!!!!!^^^^!!!!!!!!^^^^^^^^^ttttttttttzzzzzzzzzzzzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~ss~~~~~~~~~sssqtttttttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqtttttt^^^^!^^ttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~szsszzzzttttttzzzztttttttttttttttttttttzztttttzttzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzttttttzzzzzzzzzzzzzzzzzzttttttztzzzttttrttttzzzzztttttt^^^^!!!^^^zz^^^!^^^^z^^zz^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^^zz^^^^^^^^zzzzrr^^^^^^!^!^^^^^!!!!^!!!!^^^ttttttttttttttzzzzzzzzzztzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqtttttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqtttt^^^^!!!^^ttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqtttttzzzzzzztttttttttttttttttttzzzztzzztttttttzzzzzzzzzzzzzzzztzttzzzzzztttttttztzzzzzzzzztzzzzzzzztttttzzzzzttttttrrtttttztttttttt^^^!!^^^^^zz^^^!!^^zzz^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^^^^zz^^^^^^^^zzzrrr^^^^^^!!^^^^^!!!!!!!!!!!^^ttttttttttttttttzzzzzttttzzzzzzzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqttttqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqs~~~~~~~~~~~sqtttt^^^^^^^^^ttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qttttzzzzzzztttttttttttttttttttzzzzzzzztttttttzzzzzzzzzzztzzttttttttzzttttttttttttzzzzzzttttzzztzztttttzzzzztttttttttrtttttttttttt^^^^!!!!^^^^zz^^^^^^^z^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^zzzz^^^^^^^zzzzr^rrrrrr^^!!^^!^!!!!^!!!!^!!^^tttttttttttttttttztttttttzzzzzzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqss~~~~~sqttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqttqqss~~~ssssssqtt^^^^^^^^^^ttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqtzzzzzztttttttttttttttttttttttztzzzzzzttttttzzzzztzzzzttttttttttttzzzttttttttttzztttzztttzztttztzttttztztttttttttttrtttttttttt^^^^!!!!!^^^^zzz^^^^^^^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^^^^^^^^^zzz^^^rrrrrr^^^!!!!!^!!^^^!!!!^^^^ttttttttttttttttttttttttttzzzzzsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqttqqss~~~~sqtttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssssqqttttqqqssqqqsqqtt^^^^^^^ttttttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqzzzzzztttztttttttttttttttttttttttzzzzztttttzzttzzttztttttttttttttzzttttttttttttttttttttttttttttttttzttttttttttttttrtttttttttt^^^^!!!!!!^^^z^zz^^zz^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^^^z^^zz^^^^^^^^^rrr^^!!!!!^^!^^^^^^^^^^^tttttttttttttttttttttttttttzzzss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqttttqqs~~s~sqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~sqqqqqqtttttttttqqtttqtttt^^!!^^^tttttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~sqqsrrrzzzztzttttttttttttttttttttttttzzzzzzzttttttttttttttttttttttttttzttttttttttttttttttttttttttztttttttttttttttttttttrttttttttt^^^^^!^!!!!!^^^^^zzzzzzz^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^^^^^^^^^^^r^^^!!!!!^^^^^^^^^^^^^^ttttttttttttttttttttttttttzzzzs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqttttttqsss~~sss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqsrrqttttttttttttttttttttttttt^^!^^^tttqqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqqss~~~~~~sqttqtttrztttttttttttttttttttttttttttttzzzzttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttrtttttttt^^^^!!^^!!!!^^^^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^^^^^^^^^^^^^^^!!^^!^^^^^^^^^^^^^^^tttttttttttttttttttttttttttztq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~sqtttttttqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqtqrrqttttttttttttttttttttttt^^^!!^^tttqssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqttqqssssssqqttttttrttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttrttttttttt^^^^^^^^^!^^^^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzz^^^zz^^^^^^^^zzzzzzz^^^^^zz^^^^zz^^^^^!^^!^^^^^^!!^^^^^^^^^^^^^tt^ttttttttttttttttttttttttttttttttq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~sqtttttttttttq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqttttrtttttttttttttttttttt^^^^^^^!!^ttttqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssttttttqqqqqqtttttttttrtttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttrttttttttttr*^^^^^^!^^^^^^^^^^zzz^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzz^^^^^^^^^^^z^^zzz^^^^^^^^^^^^^^^^^!!!!!!!^^!!!!!^^^^^^ttttt^^^ttttttttttttttttttttttttttttttttztqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqtttttttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssssss~~~~~sqttttrtttttttttttttttttttt^^^^^!!!^^ttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqtttttttttttttttttttttrtttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttrtttttttrrr^^^^^^^^!!^^^^^^^^^^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzz^^^^^^!^^^^^^^^^^^^^^^^^^^^^^^^^^^!!!!!!!^^^^!!^^^^^^tttttt^ttttttttttttttttttttttttttttttttttttq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqttttqtttq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqqssss~~sqtttttrrtttttttttttttttttttt^^!^!!^^^ttttq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqtttt^^ttttttttttttttttrttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttCCCtttttttttttttttttttttttttttttttttttttttttttttrrttttrttt^^^^^^^!!!!!^^^z^^^^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzz^^^^!!^^^^^^^^^^^^^^^^!!^^^^^^^^!!!!!!^^^^^^^^^^^^^tttttttttttttttttttttttttttttttttttttttttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqtttqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqtttttqqqqssqqttt^ttrrttttttttttttttttttt^^!!!^^^^tttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqtttt^ttttttttttttttttrtttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttCCCCCttCtttttttttttttttttttttttttttttttttttttttttttrttrtttt^^^^^^^^!!!!^^^zzz^^^^zz^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrzzzzz^^^^^!!!!!^^^!^^^^^^!!^^^^^^^!!^!!!^^!^^^^r^^^^^^^tttttttttttttttttttttttttttttttttttttttttttqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qtqqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqttttttttttqqtt^^^^tttrtttttttttttttttttttt^!!^^^ttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqtttt^^^ttt^ttttttttttrttttttttttttttttttttttttttttttttttttttttttttttttttttttCCCttttCCCCCCCCCtttttttttttttttttttttttttttttttttttttttttttttrrtttt^t^^^^^^^!!!!^^^^zzz^^^z^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrz^^^^^^^!!!!!^^!!!^^!!^^!!^!^^^!!^^^!!!^^^^^^^r^^^^^^^tttcttttttttttttttttttttttttttttttttttttttqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqttt^^tttttttt^^^^ttttrttttttttttttttttttttt^!^^^tttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqttt^^^^t^^^ttttttttrtttttttttttttttttttttttttttttttttttttttttttttttttttttCCCCtCCCtCCCCCCCCttttCCtttttttttttttttttttttttttttttttttttttttttttttttt^^t^^^^^!!!^^^^zzzz^^^zz^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzrz^^^^^^^!!!^!^^^!!!!!^^!!!!^^^^!!!!!!!^^^^^^^rt^^^^^^^ttttttttttttttttttttttttttttttttttttttttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqtttt^^tttttttt^^^^ttttrttttttttttttttttttttt^^^^ttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqttt^^!!^^^^^ttttttttrttttttttttttttttttttttttttttttttttttttttttttttttttttCCCCCCCCCCCCCCCCCtCCCCttttttttCttttttttttttttttttttttttttttttttttttttttttttt^^^^^!!^^^^^zz^^^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzr^^^^^^^!!!^^^^^^^!!!^!!^^^^^^!!!^!!!^^^^^^^ttrtt^^ttttttctttcttttttttttttttttttttttttttttttttttq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qttqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qttt^^^^^^ttt^^^^tttttrrtttttttttttttttttttt^^^^ttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqttt^^!^^^t^^tttttttrttttttttttttttttttttttttttttttttttttttttttttttttttttttCCCCCCCCCCCCCCCCCCCCCCCCCCtCttttCttttCCtCCtttttCttttttttttttttttttttttt^ttt^^^^^^!!!^^^^z^^^^^^^^^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^rrr^^^!!!!^^^r^^^^!^^^!^^^^^^^^!!!!!^^^^^^cccrttttcchhtttcctttttttttttttttttttttttttttttttttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqttttq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqttt^^^^^^tt^^^^^ttttrrttttttttttttttttttttt^ttttttqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqttt^^!!^ttt^^ttttttrtttttttttcttttttCtttttttCCtttttttttttttttttttttttttttCCCCCCCCCCCCCCCCCCCCCCCCCCtttCtttttttCCCCCCCtttttttttttttttttttttttttttttttt^^^^^!!!!^^^^^^^^!^^^^^^^^zzzzzzzzz^zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz^^^z^^^^^^^^^!!!!^^^rr^^^^^^^^^^^^^^^^^^^^!!^^^^cccrccccthhhtthcccctttttttttttttttttttttttttttttttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqs~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqtttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqttt^^^^^^^^^^^tttttrtttttttttttttttttttttttttttttqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqtttt^^^^ttttttttttttrtttttttccCtttCCCCtCttCCtCttttttttttttttttttttttttttCtCCCCCCCCCCCCCCCCCCCCCCCCCCCtttttCCCCCCCCCCtCCCtttttttttttttttttttttttttttttt^^^^^!!!!!^^^^^^!!^^^^^^^^zzzzz^^^^^zzzzzzzzzzzzzzzzzzzzzzzzz^^^^^^^^^^^^^^^^!!^!^^^^^^riii^^^^^^^CCCC^^^^^^^^^^CCCccrccchhhhhcctcccccccctttttttttttttttttttttttttqtttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqcqs~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqtttttq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qt^^^^^!^^!!^^^^ttttrrttttttttttttttttt^^^tttttttqtqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqtttt^^^^ttttttttttttrrttttccCcttCtCCCCCCCttCCCtttttttttttttttttttttttttCCCCCCCCCCCCCCCCCCCCCCCCCCCCtCCCCCtCCCCCCCCCCCCCttttttCtttttttCttttttttttt^^ttt^^^^!!!!!^^^^^!^!!!^^^^^z^^^^^^^^^^^^zzzzzzzzzzzzzzzzzzzzzzzz^^^^^^^^^^^^^^^!!!^^^^^^iiriii^^^^^CCCCCCC^^^^^^^^CCcccrccchhhhccccccccctcccccttttttttttttttttttqqqqsqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqccqs~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qtqttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqt^^^^!!!!!^^^^^tttrrttttttttttttttttt^^^^tttttqqsqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqttttt^^^ttttttttttttttrtttccCCCCCCCCCCCCCCCCCCCCtttttttttttttttttttttCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCtCCCCCtCCttCtttttCtttttt^^^^^^^^^^!!!!!!^^^!!!!!^!!^^^^^^^^^^^^^^^^^^^zzzzzzzzzzzzzzzzz^^^^^^^!!!^^!!!!!^!!!!!!^^^^iirii^^iiiCCCCCCCCCCC^^^^^CCCcccrccchhhcccccccccctccctctttttttttttttttqqsss~~sss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqccccqs~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qsqtq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqt^^^^!^!!^^^^^ttttrttttttttttttttttt^^^ttttttqssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqttttt^^^tt^ttttttttttttrttccccCCCCCCCCCCCCCCCCtCCCCtttCCttttttttCtCCCCtCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCtttCCCCCttCtt^^^^^^^^^!!!!!!!!^!!!!!!!!!^^^^^^^!!^!!!^!!^^^^^^ztttttzzzttzttt^^^^!!!!!!^^^^!!!!!!!^^^^^iiiiiriiiiiCCCCCCCCCCCCC^^CCCCccccrcccccccccccccccccccttttttttttttttttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqcccccqs~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqxt^^!!!^^^^tttttttrttttttttttttttttt^^^^tttttqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqtttt^^^tt^^ttttttttttccrtctcccccCCCCCCCCCCCCCCCCCCCCtCCCCtttttttCCCCCCtCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC^^^^!!!!^^^^!!!!!!^^!!!!!!!!!^^!!^^^^^!!!!!^!!!!!^^^^tzztztzttttt^^^^^^^!!!!^^^^^^^!!!!^^^^iiiiiiiriiiiicCCCCCCCCCCCCCCCCCccccccrcCCCccccccccccccccccctcttttttttttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqqccccqs~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqxxt^^!^^^^ttttxtttxtrxttttttttttttttt^^^^^tttqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqtttc^^^^cc^^^ttccccttccccrrccccccCCCCCCCCCCCCCCCCCCCCCCCCCCttttCCtCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC^^^^^^!!^^^!!!!!!!!!!!!^^!!!^!!^^^^^^^^^^^^^^^^!^!^^^^^ttttttttttttt^^^^!!^^^^^^^^^^^^^^^^^iiiiiiiirciiCCCcCCCCCCCCCCCCCCCcCCccccrCCCCCCCcccccccccccctcttcttttttttttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqsssqcccqs~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggg^^^^^^^ttttttxtxxtrtttttttxttttttt^^^^^^tttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqqtttct^^!^c^^^^ttctcctctccccrccccccCCCCCCCCCCCCCCCCCCCCCCCCCCCttCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC^^^^^^^^^^^^^^^!!!!!!^^^^^^^^^^^^^^^^^^"^^^^^^^^^^^^^^^ttttttttttttttttt^^^^^^^^^""^^^^^^^^^iiiiiiccircccCCcCCCCCCCCCCCCCCCCCCCCCCcCrrCCCCcCccccccccccccccttttttttttttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qcqsssqccqs~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqgqggg^^^^^tttxtxttttxttrxtxtxxtxtttxtt^^^!!!^tttqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqtttctcct^^^^cc^^cccccctccccccrcccccCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCcCCccc^^^^c^^^c^^^^^!!!!^^^^^^^^^^^^^^^"""""""^^^"""^^^^^^ttttttttttttt"tttt""^^^^^"""""^^^^^^^^iiiiiccccrcccccCcCCCCCcCCCCCCCCCCCCCCcccCCrCCCCCCcccccccccccccctcttttttttttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqccqqssqqs~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqqgggg^^^^^^^tttxtttgggtxgrtgggxtgxxttxt^^^!!^^^^ttqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqttttttttccc^^^^^ccccccctccccccccrcccCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCcCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCcccccccc^ccccccc^^^^!!!!^^^^^^^^^^^^^^^"""""""""""""""^^^t"t"tttt""ttttttt"t"""^^""""""""""^^^^iiiiiiicccrcccccccCCCCCCCcCCCCCCCCCCCCCCCcCCrCCCCccCcCcccccccccccccttttttttttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqcccccqsss~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qggggggg^^^^^^^txttgggggtgggrxgxggggtgtxt^^^^!^^^^ttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqttttttttcc^^^^^^ccccccccccccccccrcccCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCcccccccccccccccc^^^^!^!!^^^^^^^^^^^"^^^""""""""""""""""""""""""tt""t""ttt""t"""""""""""""""^^^iiiiiiiiicccrcccccccCCCCccCCCCCCCCCCCCCCCCCCCCCrrCCCCCcCCcccccccccccccttttttttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~ssqqcccccqs~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qggggg^^^^^^^^^^ttggtgggggggrrggxggtgggg^^^^^^^^^^tttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqttttctctcc^^^!^^^ccCCccccccCccccrccccCCCCCCCCCCCCCcccCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCcCCCCCCCCCCCCCccccccccccccccc^^^^!^!!^^^^^^"""""""""""""""""""""""""""""""""""""""""t"""""""""""""""""""^^iiiiiiiiicccrcccccccccccCcCCCCCCCCCCCCCCCCCCCCCCCCrCCCCCCCcCccccccccccctttttttttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqsssqccccccqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qgggg^^^^^^^^^^tgtgggggggggrrgggggggggg^^^^^^^txttttttqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqttttttccccc^^!!!^^ccCCCCCCCCCCccrcccccCCCCCCcCCCCcccccCCCCCCCCCCCCCCCCcccCCCCcCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCcCCcCCCCCCCcCCCCCCccccccccccccc^^^^^!^^^^^^^^""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""iiiiiiiiiccccrrccccccccccCcCCCCCCCCCCCCCCCCCCCCCCCCCCrCCCCCCCCcccccccccccctttttqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqccccqssqcccccqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqgggg^^^^^^^^^^gggggggggggrrggggg^^^^^^^^^^^gtxtxxttqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqctccctcccccc^^!!!^CCCCCCCCCCCcccrcccccccCCcCcCCccccccccccCCCCCcCCCCcccCCCCCCCCcCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCccCcccCcCCCCccccccccccccccc^^^c^^^^!!!^^^^^^^^"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""iiiiiicciiccccrccccccccccCCccCCCCCCCCCCCCCCCCCCCCCCCCCCrrCCCCCcCcccccccccccctttqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqcccqsssqcccqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqggggg^^^^^^^^ggggggggggggrrggggg^^^^^^^^^^^^xggxtxtqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqtcccttccccccc^^^^^^^CCCCcCCCCccccrcccccccccccccccchcccccCCcCcCCCCCccccccCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCccCCcCCCCCCccccccCCccccccc^^^^^!!!!^!^^^^"^"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""ii"i""ccccccrcccccccCcCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCrrrCCCCCcccccccccccttqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqccccqqsssqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqggg^^^^^!^^^^ggggggggggrrggggggg^^^^!!^^^^^gxgggttqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqtcctccccpcccc^^^^^^CccCccccCCCccccrcccccccccccccchhccCcccccccCCCCcccccccccCCCcCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCcCCCccCCCCCCCccCCCCCcccccc^^^^^^!!^^^^^^^^""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""cccccrrcccccCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCrrrrrrcccccccccqqqs~~~~~~~~~~~~~~~~~~~~~~~~sqqs~~~~ssqcccccccqsssssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqggggg^^^^!!^^^gggggggggrrrggggggg^^^^^!^^^^ggggxgxxtqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~ssqcccccppppcccccc^cccccccccccCCCccccrcccccccccccchhhcccccccccCcccccccccccCCcCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCcccc^^^^^^!!!^^^^""^""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""ccccccrcccccCCCCCCCCCcCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCcCcCCcccrrcccccccqss~~~~~~~~~~~~~~~~~~~~~~~~sqccqqsssqqqcc^^cccqqsqqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqggggggg^^^^!!!^^^ggggggrrrggggggg^^^^^^!^^^^^gggggxqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssqccccpppppcccccccccccccccccCCCCccccrrcccccccccchhhhchccccccccccccccccCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCccCCCCCCCCCCCCCC^^^^^^^^!!^^^^""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""c""ccccccccrccccCCcCcCCCCCCcCCcCCCCCCCCCCCCCCCCCCCCCCCCCCCCccccccccrccccqqs~~~~~~~~~~~~~~~~~~~~~~~~sssqccqcqsqccccc^^cccccqcccccqss~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqqggggggggg^^^^!^^^^^^ggggrrgggggggg^^^^^^^!^^^^^ggggggqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssssqcccppppcccccccccc^^^^ccccccCCCcCCcccrcccccccccchhpchhhccccccccccccccCCcCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC^^^^^!^!!^^^^"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""cccc""ccccrcccccccCCCCCcCccccCCCCCCCCCCCCCCcCCCCCCCCCCCcCccccccccccrcccqs~~~~~~~~~~~~~~~~~~~~~~sqqqqqccccccqqcccc^^^ccccccccccccqqs~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqqqqqqgggggggggg^^^^!!^!!!^^ggrrrggggggggg^^^^^^!!^!!^gggggqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~ssssqpcpppppcccccccc^^^!^^^^cccCCCCCCCcccrcccccchpcpppphhhcccccccccccCCcCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC^^^!^!!^^^"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""ccccc""ccccrcccccccCCCCCCCCcccccCCCCCCCCCCcCCCCCCCCCccCCCccccCCccccccrrrss~~~~~~~~~~~~~~~~~~~~~~qcccccccccccccccc^^^^^cccccccccccccqs~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqqppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qgggggggggggggggg^^^^^!!!!!!^^^rrgggggggg^^^^^^^!!!^!!^^^ggqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssssrppppppppp^^^^^^^^^^^^^cccCCCCCCCCCcccrccccccpphhpcppccccchchcccCCCCCcCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCc^^!!!!!^^^^^"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""cc""""cccrrcccccccccCccCcccccCCcCCCCcCCCCCCccCCCCCCCCCcccCCCCCccccccqss~~~~~~~~~~~~~~~~~~~~~~sqcccccccccccccccc^^^!^^cccc^^^cc^ccqs~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qpppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqggggggggg^^^gggg^^^^!^!!!^^^^^rgggggggg^^^^^^^!!!!!!^^^^gqssssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqqqq~~~~~s~sssssRRRrpppppp^^^^!!!^!^^^ccccccCCCCCCCCCCcccrccccppphppppcccccchhhcccCCCCCCCCCCCCCCCCcCCCCCCCCCCCcCCCCCCCCCCCcCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC^^!!!!!!^^^^""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""c"""""""cccrrrrccccCCCCCCccccccCcCcCCccccCCCCCcCCCCCCCcCcCCCCCCcccccqss~~~~~~~~~~~~~~~~~~~~~~sqccccccccCcccccccccc^!!^^^^^^^^^^^ccqs~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpggppqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggg^^^^^ggg^^^^^!!!!!^^^^rgg^^^^^^^^^^!!!!!!^^!^^^^ggqsssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~qcccccqss~~ssssssssRRRRrrppppp^^^!!^^^^cccccccccCCCCCCCcccccrccccppcpcpcccccchcccccccCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCcCCCCC^^!!^^^!^^^^"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""c"""""c""cccccCCrrrccccCCccccCCccccccccccccCCCCCCCCCCCCCCCcCcCCccccccqss~~~~~~~~~~~~~~~~~~~~~~~qcccccCCCCCcCcccccc^^^!^^^!^^^^^^ccqs~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggpppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qsqgggg^^gg^^^^^^gg^^^^!!!!!!^rrrggg^^^^^^^^^!!!^^^!!!^^^^^ggqsss~s~~~~~~~~~~~~~~~~~~~~~~~~~~~qccccccqssssssssssrrppppRRRRpppp^^^^^ccccccccccccCCCCcCCcccccrcccccppccpppccccpccpcccccccCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC^^^^!^^^^^^^""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""cc""cccccccccCCCcccrrccCCccCCCCcccccCcccccCCcCCCCCCCCCcCCCccccCCccccqss~~~~~~~~~~~~~~~~~~~~~~~~sqccccCCCCCCCcccCCC^^!!^!!!^^^cccccqs~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggpppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgqqggg^^^^^^^^^^^ggg^^!!!!!!!^^^^^gg^^!!^^^^^!!!!!!!!^^^^^gggqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqcccccccqqqqsssqqqpppppppppRRrppccccccccccccCcccCCCCCCccccccrcccccccccccpppcccpccppccccccCcCCCCCCCCCCCCCCCCCCCCCCCCcCCCCCCcCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC^^^^^^^^^^^^"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""c""ccccccccCCCCCcccrcCCcCCCCCCCCcccccccCCCCCCCccCCCCCcCCCCCccccccccqs~~~~~~~~~~~~~~~~~~~~~~~~~sqqcccCCCCCCCCCCC^^!!^!!!^^^ccccqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~ss~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggpqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssssss~~~sssqdggggg^^^^^^^^^gggg^^^!^!!!!!^!^^^^^^^^!!^^^!!!!!^^^^^^^^^gqqss~s~~~~~~~~~~~~~~~~~~~~~~~~~~~qcccccccccccccqqqccccpp^^^^ppppRrpcccccccccccCCCcCCCCcCccccccrcccqqccccqccccppppccppcccccccCCCCCCCCccCCCCCCCCCCcCCCcccCCccCccCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCcCCCCCCCCc^^^^^^^^^"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""cc"""c"ccccccCCCCCCcrccccccCCCCCcccccccccCCCCCCCCCccCCCCccccccccccccq~~~~~~~~~~~~~~~~~~~~~~~~~~sssqcccCCCCCCCCC^^^^!!!^^^^ccccqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~sqqqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssssqqqqqqqqqssssqdddggggg^^^^^^^gggg^^^^!!!!!!^!!^^^^^^^^!!!^!!!^^^^^^^^^ggggqssss~ss~~~~~~~~~~~~~~~~~~~~~~~~qcccccccccccccccccccccc^^^^pp^^ppRrccccccccccCCCCCCCCCccccccccrccqllqccqlqcccpppppppcccccccccCCCCcccccCcCcCCCCCCCCCccccCCcCccCCCCCCCCCCCCCCCcCCCCCCCCCCCCCCCCCcccCCCCCccc^^^^^^^^"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""ccccc"cccCcCCccrrccccccccCCccccccccccccCCCCcccccCCCcccccccccccqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqcccCCCCCCCCCCCC^^^!^^^cccccqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~sqggggggqs~~~~~~~~~~~~~~~~~~~~~~~sqgggggggggq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqqqdddddddddqqqqqddd^g^^gg^^^^gg^^^^^^^!!!^^!!!!^!^^^^^^!!!!!!^!^^^^^^^gggggqsssssss~~~~~~~~~~~~~~~~~~~~s~~~~qccccccccccCccccccccccc^^^^p^^^^ccRccccccccccCCCCCcCCcccccccrrccccqllqcqlqcccppppppcccccccCcccCCCccccccCcCCCCCCCCCCcccccCCcCCCCCCCCCCCCCCCCCCCCCCCCCCCCcCCCCcCCccccCCCccc^^^^^c""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""cccc"""cccCCCCcccrrccccccccccccccccccccccCCCcccccccCccccccccccqs~~~~~~~~~~q~~~~~~~~~~~~~~~~~ssqcccCCCCCCcCCCCCC^^!^^ccccqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~sqgggggggqs~~~~~~~~~~~~~~~~~~~~~~~sqqgggggggq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qddddddddddddddddddddd^^^^^^ggg^^gg^^^^^^^^!^^^^^!!^^!!!^!!^^!!!!!!^^^^^^^ggggggqssssssss~s~~~~~~~~~~~~~~~~s~~s~~qcccccccccCCCcccCCcccp^^^pp^^!!^^cRrcccccccCCCCCCCCCCccccccrcccqqqllllqllqpcppppppccccccccCCCCCcCcccccCCCCCCCCCCcccccccCcCCCCCCCCCCCCCCCCCCCCcCCCCCCCCCCCCCCCCccccccCccccc^^^c""c"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""c"ccccccCCCCcccrcccccccccccccccccccccccccCccccccccccccccqqqs~~~~~~~~~sqcqq~~~~~~~~~~~~~~~~sqcccccCCCCCCCCCCCr^^CCc^cccqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~sqggggggggqs~~~~~~~~~~~~~~~~~~~~~~~~ssqqgggggq~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddddddddd^^dd^ddddd^^^^^^gggggggdd^^^^^^^^^^^^^^^^^!!!!!!^!!!!^^^^^^^^gg^^ggggqssssss~sss~~~~~~~~~~~~s~ssssss~~qccccccccCCCCcCCCccppppp^^^^!^^ccRRrccccccCCCCCCCCCCcccccrcccqlllllllllllqpppppcccccccccCCCCCCCCCccCCCCCCCCCCCCCcccccccccCCCCCCCCCCCCCCCCcCcccCCcCcCCcCCCCCCcCCCCcccccccc^^^cccc"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""ccccccCCcCcccrrcqqccccccccqqccccccccccccccccccccccccqqsss~~~~~~~~~sqccccqs~~~~~~~~~~~~~~sqccccccCCCCCCCCCrCC^Cc^^^cccqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~sqggggggggqqs~~~~~~~~~~~~~~~~~~~~~~~~~ssqgqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddddddddd^^^^^^^ddd^^^^^^ddgggggddd^^^^^^^^^^^^^^^^^!!!!!!^!!!!^^^^^^^^p^^^^gggqqssssssss~s~~~~~~~~~~~sssssqqssqcccccccccccCCCCCCcccccp^^^!!^^cccrRrccccccccCCCCCCCccccrrcccccqllllllllllqpppppccccccccccCCcCCCCCcccCCCccCCcCCcccccccccccCCCCCCCCCCCCCCCCCccccccccccCcccCCCCCCCCccccccccc^^cccccccc"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""ccccccccCCCccccrqllqccccccqllqcccccccccccccccccccccccqss~~~~~~~~~~~sqccccqs~~~~~~~~~~~~~~sqcccccCCCCCCCCCCrCCCCC^!^ccqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~ssqqggggggggggqs~~~~~~~~~~~~~~~~~~~~~~~~~~~qss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddddd^^^^^^^^^^^dddddddddddggggddddd^^^^^^^DD^^^^^^^^^!!!!!!^^!!^^^^pppp^^^ggggggqsssssssssss~~~~~~~~ssssqqccqqccccccccCccCCCCCCCccpccc^^!!^^^cccccRrcccccccccCCCcccccrcccccccqlllllllllllqppppcccccccccccCCCCCCCCcccCCcccCCCCcccccccCccCCCCCCCCCcCcCCCCCCccccccccCCcCcccCCCCCCccccccccccc^ccccccc"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""ccccccccccccccrllllqqqccqllllqccccccccccccccccccccqqs~~~~~~~~~~~~sqccccccqs~~~~~~~~~~~~sqcccccCCCCCCCCCCCCrCcC^^^!^cccqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~sssqqggggggggggggqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddd^^^^^^!!!!^^^^^dddddddddddddddddd^DDDDDDDDD^^^^^^^!^!!!!^^^^^^^^ppppp^^^gggggqssssssssss~ss~~~~~~sssqccccccccccccccCCCCCCC^^^^ccccc^^^^^^cccccccRRRrrcccccCCCCccccrccccccccqllllllllllqpppcccccpcccccccccCCCCCccccccccCCCccccccccCCCCCCCCCCCccccCCCCcccccccccccCccccCCCCCCcccccccccccccccc"cc"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""c"ccccccccccccccqllllllllqqllllllqccccccccrrrcccccccqss~~~~~~~~~~~~~sqccccccqs~~~~~~~~~~~~sqccccCCCCCCCCCCCCCrCCCCC^^^cccqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~ssqqqggggggggggggggqss~~~~~~~~~~~~~~~~~sqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddd^^^!!!!^!!!^^^^^^^dddddddddddddddDDDDDDDDDDDDDD^^^^^!!!^^^^^^^^^pppppp^^pggggqsssssssssssss~~~~ssssqcccccccccccccCCCCCCCC^^^^^^^^^cccc^^^ccccccccccRRRccccccCccccrccccccccqlllllllllqqppppccccppcccccccccCCCCCcccccCCCCccccccccccCCCCCCCCcccccccccCCcccccccccCcCCCCCCCCCCccccccccccpccccccc"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""ccccccccccccqlllllllllllllllllqccccccrRRRrcccccqs~~~~~~~~~~~~~~~qccccccppqs~~~~~~~~~~~sqccccCCcCCCCCCCCCCrCCCCCC^cccqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~sqqgggggggggggggggggqqqs~~~~~~~~~~qsssssqggq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddd^^^^^!!!^^^^^^^^^^^^^dddddddddddddDdDDDDDDDDDDDDD^^^^^^!!^^^^^^^^ppppppppppppgggqssssssssssssss~s~~ssqcccccccccccccCCCCCCCC^^^^^^^^^^cccccccccccccccccccRrcccccccccqrqccccccqlllllqqlqqppppppppcpppppccccccccCCcCccccccCCCcccccccccccCCCCCCCcccccccccccccccCCCCCCCcCCCCcCCcccccccccccppcpccp"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""c""c"ccccccqlllllllllllllllllllqqccrRRrcrRRrrRRrr~~~~~~~~~~~~~~~~qqcppcpqs~~~~~~~~~~~~sqccccccccCcCCCCCCCCrCCCCCccccqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~ssqdgggggggggggggggggggggqs~~~~~~~~qgqqsqqggggqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqdddd^^^^!!^^^^^^^^^^D^^^^^DDdddDdddddDDDDDDDDDDDDDDDDDD^^^^^!!^^^^^^^p^^^^pppppppggpqssssssssssssssssssssqcccccccccccCcCCCCCCC^^^^^^^^^^^^cccc^^ccCccccccccrRcccccccccqlllqccccccqlllqccqccpppppppppppppppcccccccCcCCcccccccCcccccccccccCCCCCCCccccccccccccccccccCCCCCCCCCccccccccccccccppccpppp"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""c"""cccccqlllllllllllllllllllllqRRrccccrrRRrrcqqss~~~~~~~~~~~~~ssqpppqs~~~~~~~~~~~~~sqcccccccccCCCCCCCCCCrCCcccccccqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~ssqsqgddddggggddgggggggggggqs~~~~~~~~qgggqgggggggqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqddddddd^^^!!^^^*DDD^^DDDDD^^^DDdDDDDddddDDDDDDDDDDDDDDDDD^^^^^^^^^^^^ppp^^^^^ppppppppppqsssssssqqsssssssssssqcccccccccccccCCCCCC^^^^!!^!^^^^^^^^^^ccCCCccccccrRcccccccccqlllqcqqccccqlqcccccpcpppppppppppppppccccccCccCcccccccCCcccccccccCCCCCCCcccpppcccccccccccccCCCCCCCcccccccccccccccpcpppp""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""cccccccqllllllllllllqllllllllllrccccccccccccccqq~s~~ssss~~~~~~~sqqppq~~~~~~~~~~~~sqpcccccccccCCCCCcCCcrCCcccccccqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~sqqdqqddddgggdgddgggggggggggqs~~~~~~~~qggggggggggggqqs~~~~~~~sqq~~~~~~~~~~~~~~~~~sqdddddddddd^!!^^^DrRDDDDDDDDDDDDDDDdDDDddDdDDDDDDDDDDDDDDDD^^^^^^^^^^ppppp^^^^^^ppppppppppqqssssqqppqssssssssssqccccccccCcccCCCCCCC^^^^!!!!!^^^^^^^^ccccCCccccccrrRrccccccqlllllqllqccqlllqccccccppppppppppccppcpccccccccccccccccccccccccccCcCCCcccccpppcccccccccccccccCCCCCcccccccccccccccpppppppp"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""cccccqqllllllllllqcqqllllllllqcccccccccccccccpqqsssssssss~~~~~ssqpq~~~~~~~~~~~~sqppccccccccCCCcccccrcCcccccccqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~sqddddddddddgggddggggggggggggqs~~~~~~~~qggggggggggggqgqsssssssqggq~~~~~~~~~~~~~~~~sqddddddddd^^^^^^DDrRrDDDDDDDDDdDDDDDDDDDdDDDDDDDDDDDDDDDDDDv^^^^^^^^^^pppp^^^^^^^pppppppppppqqqqppppqssssssssssqcccccccCCCcccCCCCCC^^^^!!!!!!^^^^^^cccccCCCccccccrrRrccccqlllllllllqcqlllqcccCccpppppppppppcccppcccccccccccccccccccccccccccCCCcccccppcpccccccccccccccccCCCCcccccccccccccpppppppcppccc"""""""p"p"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""c""ccccccqlllllllllqcccqlllllllqccccccccCCCCcccpppqsqqqqqqss~~~~~~sq~~~~~~~~~~~~~~sqppppccccccCCcccccrccccccccqsssss~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~ssqddddddddddddddggdggggggggqss~~~~~~~~~qggggggggggggggqqsssqqggggq~~~~~~~~~~~~~~sqdddddddd^^^^^^^^DDDrRDDDDDDDDDDDDDDdDDDDDDDDDDDDDDDDDDDDdDvvv^^^^^^^^^pp^^^^!^^^^^^pppppppppppppppppqssssssssssqccccccCCCCccCCCCCC^^^^!!!!!!!^^^^^ccccccCCCCcccccccrRrrqqlllllllllllqlllqcccCCCcccppppppppppccpccccccccccccccccccccccccccccccccccpppppccccccccccccccccccCcccccccccccccccpppccccccccc""cc""ppppp""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""cccccqlllllllqccccqlllllqqccccccpcccCCcccpcpppqppppppqs~~~~~~~~~~~~~~~~~~~~~~~sqppcpcccccccccccpcrccpcccqsssqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~sqddddddddddddddddddggggggggqs~~~~~~~~~~sqpppppggggggggggqqqgggggggq~~~~~~~~~~~~~sqddddddddd^^^^^^DDDDDRrDDDDDDDDDdDddDDDDDDDDDDDDDDDDDDDDDdddvvv^^^^^^^vvp^^^!!!^^^^^^ppppppppppppppppqssssssqqqssqccccCCCCCCCCCCCC^^^!!!!!^^^^^^^^^ccccccCCCCCcccccccqllllllllllllllllllqcccCCCCccpppppppccpppppppcccccccccccccccccccccccccccccccccccppcccccccccpppcccccccccccccccppccpppppccccccccccccccpppppp""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""ccccccqllllqlqccccqllllqqcccccpcpppccCCccppppppppppppppqs~~~~~~~~~~~~~~~~~~~~~~ssqppppcccccccccpppcrrpccqssqqccccqs~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~sqqddddddddddddddddgdgggggqs~~~~~~~~~~~~sqpppppgpggggggggggggggggggq~~~~~~~~~~~sqddddddddddd^DDDDDDDDDDRrDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDdddddvvvv^^^^vvvv^^^!!!!^^!^^pppppppppppppppppqssssqpppqsqccccccCCCCCCCC^^^^!!!!!!^^^^^^^^ccccCCCcCCcCCCccccccqqlllllllllllllllllqqccCCcccpccppccpccccpppppcccccccccccccccccccCCccccccpcccpppccccccpcpcpcpcccccccccccccccccppppccpccccccCCcCccccpppp""pp"p""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""c"cccrRqqqpqppccccqlllqppcccpppppcpccccpppppphppppppppqqs~~~~~~~~~~~~~~~~~~~~~~sqppppcccccccccpppppprrrssqccccccqs~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~ssqddddddddddddddddgggqqqs~~~~~~~~~~~~~ssqpppppggggpgggggggggggggggq~~~~~~~~~~sqddddddddddddDDDDDDDDDDDRrDDDDDDDDDDDDDDDDDDDDDDDDDDDDDdddddvvvvvvvvvvvvv^^^!!!!!!!!^^^ppppppppppppdpppqqsqqpppppqqccccccCCCCCCCC^^^^^^!!^^^^^^iiiccccccCCcCCCCCCCCCccccqlllllllllllllllllllqcccCcccppppccccccppppppcccccpcccccccccCCcCCCCcccccccccpppccccppppppppccpccccccccccccccccppccccccccCCCCCCcccccpp""""ppp""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""rr"ppppppppcccpqqlrpppccppppppppcccppp^ppppphhppppppqs~~~~~~~~~~~~~~~~~~~~~ssqppppcccccppppppp^ppppqqpcccccccq~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~sqddddddddddddddddgggqss~~~~~~~~~~~~~ssqpppppppggppgggggggggggggggqs~~~~~~~~~sqdddppdpddddddDDDDDDDDDDrRDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDdddvvvvvvvvv^^^^^^^^!!!!!!^^^^ppppppppppdddppppqppppppppqpccccCCCCCCC^^^^^^!!!!^^^^^iiiccccccCCCCCCCCCCCCCCccccrlllllllllllllllllqccCCCccpppppcccccccpppppcccccccccCCcccCCCCCCCCccccccccppcpcccpppcpppppppppcccccccpccccccppppccccCCCCCCCccccccppppp""ppp""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""c"rr""ppppppppppccpppqrppppppppppppppccpp^^pppphhpphppppqs~~~~~~~~~~~~~~~~~~~~~sqppccppcccpcppppp^^pppppcccccccccq~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~sqddddddddddddddddgdgqs~~~~~~~~~~~~~~sqgppppppppppppgggppggggggggggqs~~~~~~~~ssqdddppddddDddDDDDDDDDDDDRDDDDDDDDDDDDDDDDDDDDDDDDdDDDDDDdddddvvvvvv^^^^^^^!!!!!!!!!^^^ppppppppppddddppppppppppppcpccccCCCCC^CC^^^^^!!^!!^^^iii^iicccccCcCcCCCCCCCCCCccccrllqllllllllllllllqcccCCcccpppppppcccpppppccccccccccCCCCCCCCCCCcccccccccccppppppppccppppppppccccccccppcppppcppccccCCCCCCCCCCccccppppppppppp""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""rr""""pppppppppppppppprpppppppppppppppp^^^^pphhhphhpppqs~~~~~~~~~~~~~~~~~~~~~sqppcccppcccppppp^^!^ppppppccccccccqs~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~sqddddddddddddddgggqs~~~~~~~~~~~~~sqqqppgpppppppgpppppgggddgggggggqs~~~~~~~~ssqqdppdddddDDDDDDDDDDDDDhRrDDDDDDDDDDDDDDDDDDDDDDDDDDDDdDDDDDvvvv^^^^^^^^^^!^^!!^!!^^^ppppppppppppddddpdddppppppcccccccCCCC^^^^^^^!!!^!!^^^iii^^iiccccccccCCCCCCCcCCccccrRqqcqqqllllllllllllqcccCCccccpppppccpppppppcccccpccccCCCCCCCCcccccpcccccccpppppppcccccpppppppcpcppcccppppppppccccCCCCCCCCCCCCccccppppp"pp"p"""ppp""""""""""""""""""""""""""p"""""""""""""""""""""""""""""""""""""""""""""""""""""r"""pppppppppppppppppprppppppppppppppppp^^^^phhpppppppqs~~~~~~~~~~~~~~~~~~~~sqqpcccccppppcppp^^!^^pppppppccpppccqs~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~ssqdddddddddddddddggqs~~~~~~~~~~~~~qgggggpppppggpppppppgggdddggggggqs~~~~~~~ssssqdpdd^^DDDDddDDDDDDDDDhhRDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDdDvvvvv^^^^^!!^^^^^^^^^!^^^^ddpppppppppppdddppddpppp^^^cccccc^^^^^^^^^^!!!^!!!^^^ii^^^ipiiccccccCCCCCCCCCcccccrRccccccqllllllllllllqccCCccccpppppppppppppccpppppcccccccCCCCCccccccpccccccpppppppppccccppppppppppppcpppppppcccccccccCccCCCCCCccccpppppppppppppp"p"""""""""""""""""""""""""pp"""""""""""""""""""""""""""""""""""""""""""""""""""rr"""pppppppppppppppppppprppppppppppiiipp^^^^^phhhpppppqs~~~~~~~~~~~~~~~~~~~~sqppccccpppppppppp^^^^pppppppcppppppqqqs~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~sqdddddddddddddddddgqs~~~~~~~~~~~~sqggggppppggggggppgpgggddddgggggggqsss~~~ssqqqdddd^^^dDDDDdDDDDDDDDhhhRDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDvvv^^^!!^^^^^^^^^^^^^^^ddpppppppppppppddpdpp^^^^^^^ccccc^^^^^^^^!!!!!!^!^^rrrr^^iipipcccccccCCCCCCCCccccrRcccccqqlllllllllllllqcCCCCCccpppppppppppppppppppcccccccccccCccccccccpppccphpphppppppccpppppppppppppppppppppppcccpcccccccCCCCCccccpccppppcccccppp""""""""""""""""""""""""ppp""""""""""""""""""""""""""""""""""""""""""""""""""""r"""""pppppppppppppppppppprpppppppiiiiiii^^!^^pphhhppppqs~~~~~~~~~~~~~~~~~~~~qppppcccppppppppp^!^pppppppppppppppppppqs~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~qddddddddddddddqqqqs~~~~~~~~~~~~~ssqgggggpggggggggpppggdddddgggdggggqssssssqgddddd^^^^DDDDDDDDDDDDDDhhhRrDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDdDDDD^^^^^^^^^ddd^^^^dddpdppppppppp^^^pppppppp^^^^^^cccc^^^^^^^^^^!!!!!^^^^^^^iriiiiipppcccccCCCCCCCCccccrRcccccqllllllqlllllllqccCCcCCccccccpppppppppppppppppppcpcccccccccccpcpppcppphhpppppppppppppppccccpppcpppppppppccpcpccccccccCCCCcccccccccpccCcpcppp"""""""""""""""""p""""pppp"""""""""""""""""""""""""""""""""""""""""""""""""""""r""pp"pppppppppppppppppppprpppppppiiiiii^^^^!^^pphpppppqs~~~~~~~~~~~~~~~~~~~~qppppppcpppppp^pp^^^ppppqqppppppppppppppqs~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~ssqddddddddddqqqssss~s~~~~~~~~~~~~~sqggggpggggggddggppggddgggggdddggggqqqqqqggddddd^^^dDdDDDDDDDDDDDDDhhRrDDDDDDDDDDhDDDDDDDDDDDDDDDDDDDDDDDDDDD^^^^^^^dDdddd^^^ddpppdpddppp^^^^^ppppdpp^^^^^^ccccc^^^^^!^^^!!!^!!^^^^^iiirrrriipcpccccCCCCCcCCcccccrcccccccqlllqqcqllllqccccccccCCcCcccpppppppppppppppppppcpccccccccccccppppppphhhpppppppppppppccccccpccccppppppppcpppccccccCCCCCCCCCcccccccccCCcccpppp""pp"""""""""pp""""pppppppp"p""""""""""""""""""""""""""""""""""""""""""""""""r"p""pppppppppppppppppppppprpppppppiiii^^^^^^^^^^ppppdppqs~~~~~~~~~~~~~~~~~~~~qpppppppppqppp^^ppppppqqssqqpppppppppppppqs~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~sqqqdddddddqss~s~ssss~~~~~~~~~~~~sqggggggggggddddgppgggggggggdddggggpppgppgggddgdgdddddDDDDDDDDDDhDDDRrDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD^^DDdDdDddddd^^ddpppdddpppp^^!^^^^^ppp^^^!^^^cc^^^^^^^^!!!!!!!^!!^^^^ii^^^^iripccccccCccCCccCCccccrRccccccccqqqccccqllqccccccccccCCCcccppppppppppppppppppppccccccpcccccpccpppppphhpppppppppppcppccccccccccpppppppppppppcccccccccCcCcCCCcCccccCCCccppppppp"p""""""""pp"""""pppppppppp"""""""""""""""""""""""""""""""""""""""""""""""r"ppp"ppppppppppppppppppppprpppppppiiii^^^^^!!^^!^pdpdppqs~~~~~~~~~~~~~~~~~~~~~sqqqpppppqsqp^^!^^pppqsssssqppppppppppppqs~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~sssqqddddqs~~~~sssqqqs~~~~~~~~~~sqgggggddggddddgggpgggggggddddddgggpgppppggddggggdddddDDdDDDDDDDDDDrRrDDDDDDhDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDddddddppppppppddpp^^^!!!^^^pp^^^^!!!^^^^^^^^^!!!!!^^!!!!^^^ii^^^^^iiirpcccccccccCCccccccccRrcccccccccccccccqlllqrrrrrccccccCccppppppppppppppppppppppccccccccccpcccpppppppppppppppcccpccccccCccCCcccpcpppgpgggpgggccccccccCCCcCCCCCCcCCCCCcppppppppp"""""p"pp"""pppppppppppppp"ppp""""""""""""""""""""""""""""""""""""""""""r"ppppppppppppppppppppppppprppppppipiiii^^!!!!!!^^^ddddpqs~~~~~~~~~~~~~~~~~~~~~~sssqppppqsqppp^^^ppqss~sssqpppppppppppqs~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~sqddddqs~~~~ssqgggq~~~~~~~~~~ssqggggdgddddddgggppgggggddddddddgggggppgggddggggddddddddDDDDDDDDDDrRDDDDDDhhhDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDddddddppppppppppdddd^^^^^^!^^p^^^!!!^^^^^^^^^!!^^^^^^^!!!!^^ii^^^^iiiiirrcccccccccccccccccrRrcccccccccccccccqllrrppppprrpcccccccpppppppppppprrrppppppppccccpcccppcpppppppppppppppccccccccccCCCCCCCcccccpppggggggggccgpgcccccccCccccCCccCcCccpppppppp"""""ppppp"pppppppppppppppppppp"""""""""""""""""""""""""""""""""""""""""rppppppppppppppppppdddpppprpppppppipiiii^^^!!!!!^^^dddppqs~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqsssqpp^^pppqs~~~~~sqppppppppppqs~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~sqqqqs~~~~sqqqgggq~~~~~~~~~~~sqggdddddddddgdgggggggddddddddddggggggppgggggggdddddddddDDDDDDDDDrRrDDDDDDhhhhhDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDddddddpdpppdpdddpddddddd^^^^^^^^^!^^!!^^!^^!!!^^^^^^^^^!^!!^^^i^^^iiiiippprcccccccccccccccrrRccccccccccccccpcqllqpppppppprpccccccccpppppppprrppprrpppppppppppppccpppppppppppppppppppccccccCCCCcCCCCCccccpppppgggggpgggpccccccccccccccCCCCcccccppppp"p"ppppppppppppppppppppppppppppppp""""""""""""""""""""""""""""""""""""""""rppppppppppppppppdddddppprpppppiipiiiiii^^^!!!!!!^^ddppqss~~~~~~~~~~~~~~~~~~~~~~~~~~ssssssssqpppppqs~~~~~~sqpppppppqqqs~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~ssss~~~~sqggggggq~~~~~~~~~~sqgggddddddddddddggggggddddddgdddggggggpggggggggdddddddDDDDDDDDDDDRrDDDDDDDDDDDhhDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDdDDddddddpddppdpddddddddd^^^^^^^^^^^^!!^!^!^^^^^^i^^^^^!^!!!^^ii^^iiiiippcrcccccccccccrrrrrRcccccccccccccccpccqqqpppppmpprpppcccccppppppprrppppppprpppppppppppppcppppppppppppppppppppccCCCCCCccccccCcccccpgppggggggggpccpcccccccccpcccCCCccccccppppppppppppppppppppppppppppppppdpppppppp"pp"""""p""""""""""""""""""""""""""""rppdppdppppdddppdddddpppprppppiiiipiii^ii^^^!^!!!^^dddpqs~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~sssqp^^ppqs~~~~~~~sqqppqqpqss~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~sqggggggq~~~~~~sqssqqggggdddddddddddddgggggdddddggdgggdddggpgggggggdddddddDDDDDDDDDDrRDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDdDDDDdDddddpdddppdpdddddddddp^^^^^^^^^^^^^^^^!^^^^iiivrr^^!!^^^^ii^iiiiicppccrrrccccccrrccccrRccccccccccccccppppppppppmmmppprpppcccppppppprpppppppppprpppppppppppppppppppppppppppppppcccccCCCccccccccccccccppgggggggggpppppppcccpcccppccccccpcpppppppppppppppppppppppppddpppppppdddppppppppppppp""pp"""""""""""""""""""""""d"""rpppddppddppddpdddddddpprpppiiiiiiiii^^^^i^^!!!^^^^ddddrss~~~~~~~~~~~~~~~~~~s~~~~~ssqqqss~~sqp^^ppqs~~~~~sssssqqssqs~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~sqqggggqq~~~~~~sqgqqggggdddddddddddddggggggggdddgggggggdddggggggggddddddddDDDDDDDDDrRRDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDdddddpddddddddddddddddpp^^^^^^^p^^^^^^^!^^^iivvvrvv^^^^^^^^iiiiiiipcccccccrrrrrrrrccccpRRccccpccpccpccppppppppmmpmmmpppprpppcpppppppprppppppppppprrrrrppppppppppppppppppppppppppccccccccccccpppcccccppggggggggggpppppppppccppcpppppccccppppppppppppppppppppppppppddddddpppddddpppppppddpppppppp""""""""""""""""""""""""dddrrddddpddddppppppdddddppprpppiiiiiiii^^!^ii^^!!^^^^dddrdqss~~~~~~~~~~~~~~~~sqss~sssqpppqss~sqpp^ppqs~~sssssssssss~s~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~sqppgggqss~~~~~~sqgggggggddddddddddddddddgggggdddddggdgggdddggggddddddddddDDDDDDDDDrRrDDDDDDDDDDDDhhDDDhDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDddddddddddddddddddddddpdd^^^dpp^^^^^!^^^^iivvvrvvi^^^^^^^iiiiipppcccccccccccccccccccccrRccccccpppppppmpmmpppppmmmmppmmprpppppppppprrppppppppppppppppprrrrppppppppppppppppppppcccpcccpcccccppppcccpppggggggggggggpgpppppppppppppppppccpppppppppppppppppppppppdpdddddddddppdddpppppppddddppddppp"""""""""""""""""""""""dddddrrdddddddddddpddpdddpppprppppiiiiii^^!^^ii^^^!!^iddrrddqqsss~~~~~~~~~~~~~sqpqqsssqpppppqssssqpppqs~~sqqqqqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~qpppgggqs~~~~~~~qggggggdddddgdddddddddddgdgggggdddggdddggddddggddddddddddDDDDDDdDDrRrDDDDDDDDDDDDDDhDDDDDDDDDDDDDDDDDDDDDDdDDDDDDDDDDDDDDDDDDddddddddddddddDDDddddddddd^dddddp^^^!^!^iivvvrvvi^^^^^^iiiiiiiiipcccccccccccccccccccccrRcccccppppppppmmmmppppppmmmmpmmmprppppppprrpppppppmppppmpppppppppprppppppppppppppppppppcccpcccccccppcpppcpppggpggggggggpppppppppppppppppppppccppppppppppppppppppdddddpddpddddddppdddddddpdddpddddpddpp""""""""""""""""""""""""dddddddrddddDdddddddpppdpppppprpppiiiiiii^^^ii^^^!!!^irrddddddqqqss~~~~~~~~~~sqppppqsssqpppppqsssqpppqs~sqpppppppqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~qpppppqs~~~~~~~~qggggggddddgdggdddddddddddgggggggggddddddddddddddddddddDDDDDDDDDDDRrDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDddddddDDdddddDDDDDDDDddddddddddddd^^^!!!^^ivvrvvi^^^^^iiiiiiiiiiicccccccccccccccccCccccrRccccccppppppmmmmpppppmmmmmpmmmmmrpppppprpppppmmmmppppmmpppppmpmmpprrpppprrpppppppppppppcpppccccppcccppppppppgggggggggggppppppprppppppppppppppppppppppppppppppppdpddpppdddddddddpdddddddddddddddddpddppp""""""d""""""hh""""""""ddddddrdddDDddDdddppppdpppppprpppiiiiiiii^^i^^^^!^^iriidddddddddqqsss~~~~~~~~qpppppqsssqqpppqssssqqqssssqpppppppppq~~~~ssss~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~sqpppqs~~~~~~~~~qggggggggddgggggdgdddddddddggggggggggdddddddddddddddddddddDDDDDDDrRDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDddDDDDdDDDDDDDDDDDDdddddddddd^^^^^^!^^^^ivrvvi^^^^ii^iiiiiiipicpccccccccccCCCCCCcccpcRrcccppppmmmmmmmmpppmmmmmmppmmmmmprrrrrrppppmmmmmppppmmmppppmmmmmmppprrrrpprppppppppppppppcppppppcccccpppppgppgggggggggpgpgppprprrrrrrppppppppppppppppppppppppdppppppppddddddddddddDddddddddddddddpppppppp"""ddd"""h"hhh"d""ddddddddddrdxxxDDDddddppppppppppprrrpppiiiiiiii^^!!^^iiri^^DDddddddddqqs~~~~~~~~sqpppqss~sssqppqssssssssssqpppppppppppqsssqqqqs~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~qpppqs~~~~~~~~~sqgggggggggggqqggddddddddddggggggggggggddddddddddddddDddDDDDDDDDrRDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDdqqdDDDDDDDDDDDDDDDDDDDDDdDDDDDDDDdDDDDDDvDDDDddddddd^^^^^^^^^^^ivvrvii^^^^i^^^iiiiipipccccccccccccCCCCcCCccccRrcccpppppmmmmmmpppmmmmmmmmppmmmmmmpmpmmmppmmmmpppppmmmmpmmmmmmmpppppppppppprppppppppppppppppppppccpccppppppggggggggggggggpprrpppppppprrpppppppppppppppppppppdppppdddpddddddddddddDDdddddddddddddpdddppppp"""dd"ddhhddddd""dddddDdDdxxrxxSSxDDDDddpdppppppppppppriiirriiii^^^!!^^iri^^DDDdddddDddddqs~~~~~~~~sqqqss~~~sssqqssss~~~sssqpppppppppppppqqqddddqs~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqs~~~~~~~~~~~sqgggqggggqqsqggggddddgggggdgdggggggggddddddddddddddDDddDDDDDDrRrDdDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDqllqqqDDDDDDDDDDDDDDDDDDDDDDDDDDDddDDdDvvvDDDdddDDDDD^^^^^!!^^^^iivrvii^^^^^^^^iiiiipipcccccccccccccCCCCCCcccccRrcccpppmmmmmmmppmmmmmmmmppmmmmmmmpmmmmpppmmmppppppmpmmmmmmppppppppppppppppprpppppppppppppppppppppppppppppghgggggggggggggrrgggppggpgpggrpppppppppppppppppppdddppdddddddddDdddddddDDddDdDddddddddddddpppppd""ddd"dhhhdddddddddDDDDDxSrSSSSxDDDDDDddpppppppppppppprrpiiriiii^^^^^iir^^^DDDDDddDDdddddqs~~~~~~~~~sssssssssssssss~~~~~ssqpppddpppppppqqddddddqs~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~~~~~sqqqsqqqqsssqggggddgggggggddddggggggdddddddddddddDdDDddDDDDDrRrDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDqlllllqdDDDDDDDDDDDDDDDDDDDDDDDDDDdDDDDDvvvDDDddDDDDdi^^^!!!!^^^^ii*ii^^^^^^^^ii^iiiipppccccccccccCCCCCCcccccccRrccccppmmpmmmpppmmmmmmmppmmmmmmmpmmmmmmpmmmpppppppppmmmmmpppppppppppppdppppprppppppppppppppppphpppppppppphhhggggggggggrrggggggggggggggprppppppppppppppppppppppddddddddddDddddDddDDdDDdDdddddddddddpddpppppddddddhhhdddddddddDDDxxxSrSSxSSxDDDDDddddpppppppppppppiiiiiriiii^^^^iir^^^^^^dDDdDddddddqs~~~~~~~~~~~ss~~ssqsqqqss~~~~ssqpppddhphpppppppddddddqs~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~sssssssqgggggggggggggdddgggddgdddddddddddDDddDDDDDDDDDrrRrDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDqlllllllqDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDvvvvDDDDdDDDDDii^^^^!!!^^^^^iri^^^!^^^i^^^^^iippcccccccccccCCCCCccccccccRrccccpppppmmmmpmmmmmmmmmmmmmmmmpmmmmmmmpmmmppppmmmmmmmmmmpppppppmppppddppppprpppppppppppppppppppppppppppphhhhgggggggrrgggggggggggggggggrpppppppppppppppgpppppppddddddDDDDDDDDDDDDDDDDDddDDDDDdddddddddddppddddddddhhddddddDDdDDxSSSSrSSSSxDDdddddddppppppppppppiiiiiiiriiiii^^ir^^^^^^^^DDdDDddddddq~~~~~~~~~~~~~~~sqdqdddqssssssqpppddhhhppddppdddddddddqs~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~sqgqqggggggggddddggddddddddddddddDDDDDDDDDDDDrrDRrDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDqllllllllqdDDDDDDDDDDDDDDDDDDDDDDDDDDDDDvvvvDDDDDDDDDDDDii^^^!!!^^^^^iri^^^!^^^^^^^^^iipppccccpcccCCCCCCcccccccccRrcccccpppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmpppppmmmmpppddpppppprpppppppppppppphhhpppppppppppphhhggggggrggggggggggggggggggggrgpppppppppgppgggpppdpppdddddDdDDDDDDDDDDDDdDDdDdDDDdddddddddddpdpddddddddhhddDDdDDDxDxSSSSSrSSSSSxxxdddddpdpppppppppppppii^^^^rirriiirr^^^^^^^^DDDDDDdddddqs~~~~~~~~~~~~~sqdddddddqsssssqppddddhhpdddppddddddddddqs~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqssqqgggggggggdgggddddddddddddddDDDDDDDrrrrDDDRrDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDdqllllllqqDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDvvvvDDDDDDDDDDDiii^^^^^!!^^^^ir^^^^!^^^^^^!^^iippppcccppccCCcCCcccccpccccrRcccccpppmppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmpmmmmmmmmppddpppdppprpppppppppppppphhpppppppprrrppggggrrrrgggggggggggggggggggggrgppgpppppppggggggpddppppddddDDDDdDDDDDDDDDDDDdDDDDDdddddDdddddddddddddhdddddDDDDDDDDxxSSSSSrrSSSxxSxdrrrppppppppppppiiipp^^^!^^r^^rrr^^^^!^^!^DDDDDdddddddqs~~~~~~~~~~~~~sqddddddddqssssqppddddhhdhdddddddddDdddddq~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~sqggggggggggggggdddddrrrrrrrrrrrrrrrDDDDDDDrRrDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDdqlllrqqDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDvvvvDDDDDDDDDDDDiii^^^^^!!^^^^^r^^^!!!^^^^^!^^iiipppppppccccCCCcccccccccrRRrcccccpppppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmpppppdddppprppppppppppphppppppppppppppprrrrrrgggggggggggggggggggggggggrgggppppppgggggdddddppppdpddddDDDDDDDDDDDDDDDDDDDDddDDDDDDDdddddddddddddddddddDDDDDdxxSxSSSSSrSSSSSrrrppprpppppppppiiiiiiiii^^!^r^^^^^^^^!!!!^^DDDDDdddddddqs~~~~~~~~~~~~~sqdddddddddqs~ssqqqddddddddddddDdddDDddddqs~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqggggggqggddggddddrpddddddDDDDDDDDDDDDDDDDRrDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDdqllqrDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDvvvvvDDDDDDDDDDiiiii^^^^^!^^^^^r^^^!!!!^^!!^^^iiiipppccppccccCCccccccccrRRcccccpppppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmpddppdddddppprrpppppppppppppppppppppppppppppppggggggggpggggggggggggggggrgggggpppgggdgggdddppppdddddDDDDDDDdDDDDDDDDdDDDDDDDDDDDDDDdddddddddddddddddddddDDxxSSSSSSSSSrrrrrrdpppppprpppppppipiiiiii^^^^^r^^^^^!^^^!!!^^^^DDDdddddddqs~~~~~~~~~~~~~~~sqdddddddqss~~ssssqdddddddddddDDdDDDDdddqs~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~sqss~~~~~~~~~sqqqqqqsqqddgddddrdddddddddddDDDDDDDDDDDDDrRrDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDqqDDrDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDvvvvvDDDDDDDDDDDDiiiii^^^^!^^^^^^^^^!!^!!!!^^^^^^iiiccccccppcccCcccccpcrRRrccccpppppppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmdddddddddddpppprppppppphhppppppppppppppppppppppgggppggggggggggggggggggggrgggggpgggggdddddpddpddddddDddDDDDDDDDDDDDDdDDdDddDDDDDDDDDDDDddddddddqqdddddddddxxxSSSSSSSrrSSSSSxdpppppprppppppiiiii^^^^^^lll^!!^!!!!!!!^^^^dDDDdddddddqs~~~~~~~~~~~~~~~sqddddddqss~ssssssqdddDdddDDdDDDdDDDDDddqs~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqqqgqqqs~~~~~~~~~~~~ssssqddddrrrddddddddddddddDDDDDDDDDDDDrRDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDrDDDDDDDDdDDDDDDDDDDDDDDDDDDDDDDDDvvvDDDDDDDDDDDDDDii^^^^!!!^^^^^^^^^^!!^!!!!^^^^^^^ccccccccccccccccpprRRcccccppppppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmdddddddddddppppprrrppphhpprrrppppphhpphhhhhpppgppppggggggggggggggggggggggrrggggggggddddddddddddddddddddDDdDDDDDDDdddDddddddDDDDDDDDddddddddddqllrrrdddddddxSSSSSSrrSSSSSxxxddppppprppppippi^i^^^^^llllll!!!!!!!!!!^^^DDDDDddddddqss~~~~~~~~~~~~~~~~sqdddddqsssqqsssqddddDDDDDDdDdDDDDDDDdddqs~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qggggggggqss~ss~~~~~~~~~~ssqdrrddddddddppddddddDDDDDDDDDDDDDDrRDDDDDDDDDDDDDDDDDDDDrrDDDDDDDDDDDDDDDDDDrDDDDDdddDDdDdDDdDDDDDDDDDDDDDDDDvvvvvDDDDDDDD^DDiii^^^^!!!!^^^^^^^^^!!!!!!!!^^^^^cccccccccccccppccprRrccccccppppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmpddpdddddpppppprppprrpppprpppppppppphhhhhhpppgppppggggggggggggggggggggggggrrgggggggdddddddddddddddddddddddDDDDDDDDDdddddddDDDDdddddddddddddddqllqddrrrdddxSSSSSSrSSSSSSSxdddppppppprrpiiii^^^^!!^^lllllll!!!!!ll!^!^^DD^dDdddddqs~~~~~~~~~~~~~~~~~~~sqqqddqssqddqssqddDDDDDDDDDDDDDDDDDddddqs~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qgggggggggqqsqqqs~~~~~~~~ssrrdddddddppppdddddddddDDDDDDDDDDDDrRDDDDDDDDDDDDDDDDDDDDDDrrrrrDDDDDDDDDDDDDDrDDDDDddDdddddddDDDDDDDDDDDDDDDDDDvvvDDDDDDD^^^DDii^^^^!!!^^^^^^^^^!!!!!!^^^^^^^^ccccccccccccccppprRrrccccccppppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmpppppddpppprrrpppppprprrppppppppppphhhhhpppppppggggggggggggggggggggggdgggggrrrrrrrddddddddddddddddddddddDddDdDDDDddddddddDDddddddddddddqqqdqllqdddddrrrddxrrrrrSSSSSxxxddddddpppppppriiii^^^!!^^llllllll!l!!lll!^!^^^D^^dDDddddqs~~~~~~~~~~~~~~~~~~~~ssqqssqddqssqddDDDDDDDDDDDDDDDDddddddqs~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qgggggggggggqggdqs~~~~~~~~sqdddddddddpddddddddddDDDDDDDDDDDDDRrDDDDDDDDDDDDDDDDDDDDDDDDDDDrDDDDDDDrrrDDDDrDDDDDDdddddDddDDDDDDDDDDDDDDDDDDDDDDDDDDDD^^^Diii^^^!!!!!^!!^^^^!!!!^^^^^^^^^^ccccccccccccppppprRrcccccccpppppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmdmmpdpppppprpppppppppprrppppppphppphhhhpppppppggpgggggggggggggggggggggggggggggdddddrrrddddddddddddqqddddDdddDddDDDDdddddddddddddddqddqqqlllqllllqdddddddrrrrddxSSSSxxddxdddddddpdpppiriiiii^^^^^lllllllllllllll!!!!^^^^^^dDDdddddqs~~~~~~~~~~~~~~~~~~~~~~ssqdddqssqddddDDDDDdDdddDDdDddddddqs~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqgggggggggggddqs~~~~~~~~sqddddddpdpdddddddddDdDDDDDDDDDDDDDRrDDDDDDDDDDDDDDDDDDDDDDDDDDDDrrrrDDrDDDrDDDrDDDddddddddddddDDDDDDDDDDDDDDDDDDDDDDDDDD^^^^D^^ii^^!^^!!!!!^!!!!!!^^^^^^^^^cccpccccccccccppppRRppcccccppppppmmmmmmmmmpmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmppdddppprppddpppppppppppphhhhhhppppppppppppggggggggggggggggggggggggggggggggdddddddddrdddqddddddqllqqddDdddDdddDDdddddddddddddqqqlqqllllllllllqddddddddddddddxSxxxxddddddddddddppppiiriiiii^^^llllllllllllllll!!!!!^^^^^DDDdddddqs~~~~~~~~~~~~~~~~~~~~~~~~qddqssqdddddDDdddddddDDddddddddqs~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqggddgggggdddqss~~~~~~~~qdddddddddddddddddddddDddDDdDDDDDrRrDDDDDDDdDdDDDDDDDDDDDDDDDDDDDDDDrrdddddrrrrrrrrrrdddddddddDDDDDDDDDDDDDDDDDDDDDDDDDDD^^D^^^^i^^^^^!!!!!^!!!!^^^^^^^^ccccccccpcccccppppprRRrpcccccppppppmmmmmmmmppppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmpddddpprpppdpppppppppppphhhhhhprppppppppppppgggggggggggggggggggggqdggddddgddddddddddrrqqlqdqqqqlllllqdddddDddddddddqddddddddqlllllllllllllllllqddddddddddddxdxxxdDDDDddddddddpppppiiirriiii^^lllllllllllllllll!!!!!^^^^dDDdddDdqss~~~~~~~~~~~~~~~~~~~~~~~~qqsssqdqqdddddddddddddddddddqqs~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggddddddddddqqs~~~~~~~sqddddddddddddddddDDddddDDdddDDDDRrDDDDDDDDDddDDDDDDDDDDDDDDDDDDddDdDDDddddddddddddddrrdddddddDDDDdddDddDDDDDDDDDDDDDDDDDDD^^^^^ii^^^^^^^^!!!!!^^^^!!^^^cccccccccccccccppprRrpppccccppppmmmmmmmmppppppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmppddppprppppppppppppppppppphhhppprppppppppppggggpggggggggpgggggggqlqgdddgdddddddddddddqllllqllllllllllqddddddddddddqlqddddddddqllllllllllllllllqdddddddddddddDddxDDDDDdddddddppppppiiiririi^^^lllllllllllllllll!!^!!!^^ddDDDdddddqqs~~~~~~~~~~~~~~~~~~~~~~~~s~sssqssqdddddddddddddddddqss~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qggdddddddddddddq~~~~~~~~sqdddddddddddddddDDDddddddddDDDrRDDDDDDDDDDDDDDDDDDDDDDDDDDDDDdDDDDDDDddDDddddddddddddrdddddddDdDDDdDdDDDDDDDDDDDDDDDDDDD^^^^^^^ii^^^^^^^!!!^!^^^^^^^^cccccccccccccppppprRRpppppccppppppmmmmmpmppppppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmppppppprpppppdpppppppppppppphhpppprrpppppppppppppggggpgpggggggggqllqgddddddDDDDDdDdddddqlllllllllllllqddddddddqddddqlqdqdddddddqllllllqqllllllqddddDDdddddddDdddDDDDDddddddddpppppppipriirrr^^lllllllllllllllll!!!!^!^^ddDDDDddddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~sqddddddddqqddddddddqs~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqqddddddddddddq~~~~~~~~~sqqddddddddddddddDDdddddddDDDDDRDDDDDDDDDDDDDDDDDdDDDDDDDDDDDDDdDDddddDDDDddddddddddddrdddddddDDDDdddDDDDDDDDDDDDDDDDDD^^^^^^^^^i^^^^^^^^!^^^^^^^^^^^ccccccccccccppppprRrpppppppcppppppmmmmmmppppppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmppppprpppppdddpppddpppppppppppppppprpppppppppgppgggggpggggggggqlllqdgdddDDDdDDDdDddddqllllllllllqlllqdddddddqlqqqqlllqlqqddddqlllqllqppqlllllqddddDDDDdDDDDDDDDDDDDDDDDddddddpppppppiri^^^^rrllllllllllllllll!!!!!^^^^dDDDDDDddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddqssqqddddddqs~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqqqqqddddddq~~~~~~~~~~~sqqddddddddddddddddddddDDDDDDRDDDDDDDDDDDDDDDDDdDDDDDDDDdDDDDDDDdddddddDDddddddddddqlqddddddddddddddDDDDDDDDDDDDDDDDD^^^^^^^^ii^^^^^^!!!!^^^^^^^^pppccccpcppccppppppRRpppppppppppppppmmmmmpppppppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmppppppprpppppddpppdddddpdpppppppppppprpppppdpppppppgppgggggggqqgqlllqdddddDdDDdDDDDdddddqlllllllqqdqlqddddddqqlllllllllllllqdddqllqpqqppppqlllqddddDDDDDDDDDDDDDDDDDDDddddddddddppppppiri^^^^^^llllllllllllllll!^!^^^^^ddDDDDDDDddddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qddddddqs~~ssqddddqs~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssssssqddddqs~~~~~~~~~~~~ssqdddddddddddddddddddDDDDDDRDDDDDDDDDDDDDDDDdDddDdDDDDDddDDDDddddddddddddddddddddqllqdddddddddddddddDDDDDDDDDDDDDDDD^^^^^^ii^^^^^^^!!^^^^^^^^^pppppppccpppppppppprRpppppppppppppppmmmmppppppppmmpmmmmmmmmmmhmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmpmmppppprrrrpppppppddpppddddppppppppppppppprppdpppppppppppppgggqqqllqlllllqdddddddDDDDDDdddddqllllllqdddqllqqdddddqlllqqllllllllqddqllqppdpdpppqllqqdddDDDDDDDDDDDDDdDDddDdddddddddpppppppppir^^^^^^^llllllllllllll!!^!^^^^^dddDDDDDdDdddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqdddq~~~~~~sqqqqs~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqdddqs~~~~~~~~~~~~~sqddddddddddddddddDdDDDDDDrRDDDDDDDDDDDDDDDDddddddddDDddddddDddddddddddddddddddddqlllqdddddddddddddDDDDDDDDDDDDDdDDDD^^^^ii^^^^^^^!!!!^^!^^^^pp^^ppppppppppppppprRpppppppppppppppmmmmppppppmmmpppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmpprrrpppppppppppppppddddddpppppppppppppprpdppdddppppppppgggqllllllllqqllqqqdddDDDDdDDdddddqlllllqdddqlllllqdddqlllqdpqllllllllqqlllqdpppppqqllqdddddddDDDDdDDDDDDDDddddddddpdddpppppppppiiir^^^!!^^llllllllllll!!!!^^^^^^dddDDDDDDDdddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqdq~~~~~~~ssss~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssssqqqs~~~~~~~~~~~~~~~sqddddddddddddddddDDDDDDDrRDDDDDDDDDDDDDDDDdddddddddddddddddddddddddddddddddddddqllllqqddddqdddddddDDDDDDDDDDDDdddDD^^^^i^^^^^^^^!!!!^!^^^^ppp^^^^ppppppppppppqlRqppppppppppppppmpppppppppmppppmmmmmmmmmhhmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmpmpprppppppppppppppppppppdddpppppppdpdpdppprpppddddppppppppgpddqqlllllqddqllllqddDddddDdddddqlllllllqqqllqqlllqqqlllqddqlllllllllllllqddpppppqllqdddddddDDdDDDDDddddddddddddddddppdddppppppiiiir^^^^!^^llllllll!!!!^^^^^^^^d^^ddddDDDddddddqqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~sssqqqqss~~~~~~~~~~~~~~~~~~sqdddddddddddddddddDDDDDDDRDDDDDDDDDdDDdDddddddddddddddddddddddddddddddddddpddddqllllllqddqlqdddddddDddDDDDDDDDDdddddd^^i^^^!^!!!^!!!!^^^^ppp^^^^^ppppppppppppqlllqpppppppppppppppppppppppppppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmpmmmmmmmmmppprrpppmmppppppppppppppppppppppppppdpdddppprppdddddddppppddppddddqllllqdddqllqdddddddddddddqllqlllllllllqddqlllllllllqqlllllllllllqqqddddpqqqlllqddddddDDDDDDDDdddddddddddddddpppdddppppppiiii^ir^^^!!^^llllll!!!!!^^^^^^^^d^^^^dddDDDdddddddqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqqDDDDqs~~~~~~~~~~~~~~~~~~sqdddddddddddddddddDDDDDDDRDDDDDDDDDDDdddddddddddddddddddddddddddddddddddpdddddqllllllllqqllqdddddddddDDDDDDDDDDdddddddii^^^^!!^!!!!!^^^^^p^^^^^^ppppppppppppqlllllqpppppppppppppppppppppppppmmmpmmpmmhhhmmmmmpmmmmmmmmmmmmmmmmmppmmmmmmmmmmprppppmmmmpppppppppmmppppppppdppdppppddpppprdpddddddddppddppdddddqlllllqdddqlqddddddddddddqllqdqllllllqqddddqlqqlllllllllllllllllqdddDddqqlllllqdqqdddddDdDDdDdddddddddddddddddpppdddppppiii^^^^^r^^^!!^!llll!!!!!!!^^d^^ddd^^^^^dddDDddddddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqDDDDDDDqs~~~~~~~~~~~~~~~~~~sqddddddddddddddddddDddDDrRrDDDDDDDDdDddddddddddddddddddddddddddpddddddddppddddqllllllllllllqddddddddDDDdDDDDDDddddddddd^^^!!!!!^!!!!^^^^pp^^^^^pppppppppppppqllllllqqppppppppppppppppppppppmmpppmppmmhhhhmmmpppmpmmmmmmmmmmmmmrrrpmmmmmmmmpprpppppmmmmmmpppmmmmmpmpppppppddddppdpdppprddddpdddddpppppddddddqlllllllqqdqllqdqqqdddddddqlqdqllllllqddddDddqddqllqqlllllllllllqddDDDddqlllllllqllqdddddDDDddddddddddrrrrrrrrrppppddpppiiiii^^^^*r^^^!!!ll!!!!!!!^^^^^ddd^^^!!^^dddddDdddddddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqDDDDDDDq~~~~~~~~~~~~~~~~~~~sqdddddpddddddddddddddDDdRrDDDDDDDDdddddddddddddddddddddddpppdddddddddpddpppdddqlllllllllllllqddddddddddddDDDDddddddddddd^^^!^^^^^!!^^^^^pp^^^ppppppppppppppppqlllllllqqpppppppppppppppppppppppppppmmmmhhhmmmpppmpmmmmmpmmmmpprppprppmmmpmppprpppppmmmmmmppmmmmmmmmppppppddddddppdppprdddddddddddpppppdddddqllllllllllqllllqllqdddddddqllllllllllqddDDDddddpqlqddqlllllllllllqdddddqllllllllllqdddddddDDDdddddddrrpppppppprrrpppppppiiiiii^^^^^r^^!!!!!!!!!!!!!^^^^dd^^!^!!!^^ddddDdddddddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqDDDDDDDq~~~~~~~~~~~~~~~~~~~sqddddddddddddddddyydddddRrddDDDDDDDDdddddddddddddddddddddddpppdppddppddpdpppppdqqlllllllllllqdddddddddddddDDDddddddddddd^^^^^^r^^!^^!^^^pp^^ppppppppppccccppppqllllllllqqpppppppppppppppppppppppppmmmmmmhhmmpppppmmppppmmmmprppppprpmpmppppprpppppmmmmmmmmmmmmmmmpppdpppddddddddpdpprddddddddddddppppppddddqqqqllllllllqplllllqqqdddqllllllllllllqddDDdddppqlqddqllllllllllllqqqqqllllllllllqdddddddddddddddddrppppppppppppprrpppppiii^^^^^^^^r^^!!!!^!!!!!!^!^^^dd^^^^^^^!^^dddDdDddddddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqDDDDDqqs~~~~~~~~~~~~~~~~~sqqddddddddddddddydyyyydyyrRDdddDDDDDDddddddddddddddddddddddpdpppddpdpppppppppppppppqlllllllllllqddddddddddddddddddddddddd^^^^^rr^^^!^^!^^^^^pppppppppppccccccppqlllllllllllqpppppppppppppppppppppppp^^^mmmmmmmppppmmmppppmmppprpppmmrrpppppprrppppmmmmmmmmmmmmmmmmmppdddpddddddppdpdprddddddddddddppppdddddddddddqlllqqlllqllllllllqqqllllllllllllllqdDDddppqllqddqllllllllllllllllllllllllllllqdddddddddddddrrrpppppppppppppppprrppppi^^^^^!^^^^^^!^^!!!^!!!!^!^^^^dd^^^^d^^!^^^dDdDDdddddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqDDDDqs~~~~~~~~~~~~~~~~~sqddddddddddddyydddyyyyyyyrRRddddddDDDddddddddddddddddddddddddddpppdpppppppppppphhppqlllllllllllllqqpdddddpddddddddddddddpd^^^^r^^^^^!!!^^^^^^^ppppppppcpccpccccqlllllll^^lllqppppppppppppppppppppppp^^!^^^mmmpppppmmmmpppmppprrpmmmmmpprrrrrrpppmmmmmmmmmmmmmmmmmmmmmppddddddddddddddrdddddddddddddppddpddddddddddqllqddqllllllllllllllllllllllllllllqdddddppqlqppqlllllllllllllllllllllllllqqqlrrrdddddddddrrrppppppppppppppppppprrr^^i^^^^!!!!^^!!^^^^!!!!!!!^^!^^^^ddddddd^^^^ddDDdDdddddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqq~~~~~~~~~~~~~~~~~~~sqddddddddddyyydddyyyyyyyRRryddddddDDddddddddddddppddddddddddddddpppdpppppppphhhhhpqlllllllllllllllqqqdqqqqppdddddddrrrrpd^^rr^^^^^!^!!^^^^^^^^pppppppccccccccqllllllll^^^llqppppppppppppppppppppppp^^!!!^^mppppppmmmpppppprrmmmmmmmmmpppppmmpmmmmmmmmmmmmmmmmmmmmmmmmppdddddddddddddrddddddhdddpddpddddddddddddddqlqddqlllllllllllllllllllllllllllllqpdddppqlllqqlllllllllllllllllllllllqqqdddqddrrrdddddrrdddpddpppppppppppppppppr*r^^^^!!!^!^^^!^^^^^!^^!!!!^^!^^^^ddddDDddDDddddDddddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~sqqqqqqqdyyyyyydyyyyyyyrRryyyyddddDddddddddddddppddddddddddddddddppppppppphhhhhhhhpqlllllllllllllllllqllllqqqdddddrddddr*rr^^^^^^!!!!!^!^^^^^^^^ppppccccccccpqllllllll^!^llqpppppp^^^ppppppppppppppp^^^^^^ppppppmmppprrrrrmpmmmmmmmmmpmmppmmmmmmmmmmmmmmmmmmmmmmmmmmmpdpddddddddddddrdddddddddddddddddddddddddddddqddqlllllllllllllllllllllllllllllllqpddpqllllllllllllllllllllllllllllqddddddddddddrrrrrrdddpdddpppppppp^^ppppppp^^^r^^!!!!!!!^!!^^dd^^^^^!!!!^^^^^ddddddDDDDDDddddddddddqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssssssqyyyyyyyyyyyyyrRyyyyyyydDdddddddddddddpdpddddddddddddddddpdpphhppppphhhhhhppqllllllllllllllllllllllllqdprrdddddr^^r^^^^!!^!!!!!^^^^^^^^ppppppppcccccppqllll^ll^!!^l^^^ppp^^^^^pppppppppp^^pppp^^pppppppppppprppppppmmpmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmppppddddddddddddrdddddddddhddddddddddddddddddddddddqqqlllllllllllllllllllllllllllllqpppqlllllllllllllllllllllllllllqdddddddddddddddddddddpppdppppppp^^^^^piiip^^^^^^^!!!^!!!!!^^^d^^^^^!!!!!^^^ddddDdDDDDDDDDDdddddddqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqyyyyyyyyyyyrRRyyyyyyydddddddddddddddpdppdpdddddddddddpdppphhhhhppphhphhhhhppqllllllllllllllllllllllllrrddddddd^^^r^^^^!^^!!!!^^!!^^^^^pppppppcccccccprll^^^^rr^^^r^^^^p^^^^^^^^pppp^^^^^^pppppppppppppprrrrppmppmmmppmmmmmpmmmmmmmmmmmmmmmmmmmmmmmmmmmmmpmpppddddddddddddddrdddddddhhddddddddddddddddddddddddddqllllllllllllllllqllllllllllllqppqlllllllllllllllllllllllllllqdddddddddddddddddddddppppppppppp^^!!^iiiiii^^^^^^!^^^^^!!!!^^d^dd^^^!^^^!^^^dddDDDdDDDDDdDdddddqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqyyyyyyyyyyyrRryyyyyyyydddddddddddddddpdppppddddddddddddppppphhhhpppppppphhhhpqllllllllllllllllllllllqqdddddddd^^^r^^^^^!^!!!!^^^^^^^^^^^ppppcccccccccprrl^^^^^rr^r^^^^^^^!^^^^^^^^^^^^^^^^ppppp^^^ppppprdddpppmmpmmmppmmmmmppmmmmmmmmmmmmmmmmmmmmmmmmmmmpppppdddddddddddddddrdddddddhhhddddddddddddddddddddddddqlllllllllllllllqqdqqlllllllllllqqlllllllllllllllllllllllllllllqqqdddddddpddddppddddppppppppppp^!!^^^iiiii^^!^^!!^^^^^^^!!^^^^dddd^^^^^^^^ddddddddDddddddddddqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqyyyyyyyyyyqRRyyyyyyyydyddddddddddddpdddpppdddddddddddpppppphhhhhpppppppphhhhppqllllllllllllllllllllqdddddddddd^^r^^^^^!^!!!!^^^^^^^^^^^pp^pccccccc^c^^rrr^^^^^^rrr^^^!^^^^!^^^^^^^^^!!^^^pppp^^^^^^ppprddddppppppmmppmmmmmppppmmmmmmmmmmmmmmmmmmmmmmmmmppppddddddddddddddddddrddddddhddhdddddddddddddddddddqqqqlllllllllllllllqdddddqlllllllllllllllllllllllllllllllllqqqqqllllllqqddddddddppdppdddpppppppp^^^^!!^^iiiii^^^!!!!^^^^^^^^^^^^^dd^^dddd^^^^^^^ddddddddddddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqyyyyyyyyqsRqyyyyyyyydddddddddddddpdddddpdddddddddddpdpppphhhhhhhppppppppphpppqllllllllllllllllllllrdddddddd^^^^r^^^^^^^!!!^^^^^!^^^^ppp^^^cccc^^^^^^^rr^^^!^^^rr^^^!!!!^^^^^^^^^^^^!!^^^ppppp^^!!^pprrdddpppppppmpppmmmmpppppmmmmmmmmmmmmmmmmmmmmmmmmmmppddpdddddddddddddddddrdddddddddddddddddddddddddddqlllllllllllllllllllqdddddqqllllllllllllllllllllllqqqllllllqdddddqlllllllqddddddpddddppppppppppp^^^^^^^^iiiii^^^^!!^^^^^^pddd^^^^dd^^^^ddddd^^^^^dddddddqqqqqqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqyyyyqssssqyyyyyyydddddddddddddddddddddddddddddddddpphhhhhhphhpppppppppppppqllllllllllllllllllqqdrrddddd^^^^^r^^^^^^^!!!^^!!!!^^^ppp^^^^^^^^^^^^^^rrr^^^!!^^rr^^!!!^!^^^!^^^^!!!!!^^^^^ppppp^^!^^prdddddpppddppppppmmpppppmmmmmmmmmmmmmmmmmmmmmmmmmmppddddddddddddddddddddddrrrdddddddddddddddddddddddqlllllllllqqlllllllllqdddddddqlllllllllllllllllllqqpppqllllqdddddqlllllllllqdddddppddddppppppppp^^^!^^^iiiii^^^^^!!^^^^^ppppddddddd^^!!^^^dddd^^^ddddppdqsssssssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqyyqss~~~sqyyyyyyyddddddddddddppdddpdddddpdddddddppphhhppppppppppphhppppppqlllllllllllllllllqdddddrrd^^^^^^r^^^^^^^^!^^^!!!^^^^^ppp^^^!^^^^^^^^^^^r^^^!!^^^r^^^!!!^!!!!!!^!^!!!!^^^^^^^ppppp^^^prpddddpdpddddpppppmmppppppmmmmmmmmmmmmmmmmmmmmmmmmmmddddddddddddddddppdddddddrrRRRRRRRRrdddddddddddddrllllllllqddqllllllqqdddDDdddqqlllqllllllllllllqqppdpppqllqddddddqllllllllqdddppppdddddppppppppp^!!^iiiiii^^^^!!!!!^^^^ddpp^^^^ddddd^^^!^pdddddd^dpdddppqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qdddddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqs~~~~~sqyyyyyyyydddddddddddpppdpddpdppdddddddddppphppppppppppphhhhpphhppqrllllqllllqllllllqddddddr^^^^^^r^^^^^^!!!!!!^!^^^^^pppp^^!!^^^^^!^^^^rr^^^!!^^^r^^!!!!^!!!!!^!!!!!!!!^^^^^^p^ppppppprpdddddddddddpddpppppppppmmmmmmmmmmmmmmmmmmmmmmmmpmmdddddddddddddddppddddddddrRrrrddddrRRRRRrddddddrRRrqqqqlllqddqlllllqdddddDDdddddqlqdqllllllllllqddppppppqllqddDddqlllllllqqdddppdddddddddpppppp^^^!^^iiiiii^^^^!!!^^^^dddpp^^!!^pdddddd^^^dpdddddddppppqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~sqyyyyyyyyyddddddddddpppddppppppddddddddpppppppppppppppphhhhhhhhpppRrllqdqlqqdqqllqldddddddprr^^^r^^^^!^^!!!!!!^^^^^^^^ppp^^^^^^!^^!^^^^rr^^!!!^^rr^^!!!^!^^^^^^!^^!!!!!!!!^^^^^^^pppprpddddddddddpddddpppppppppmmmmmmmmmmmmmmmmmmmmmmmmppddpdddddddddDDddddppdddddrRrdddddddddddrrRRrrdrRRrddddddqqllqqlllllqdddddDDDDddddqlqdqllllllllqqdddpdppppqlqddDDdddqqlllqqddddpddddddddddpppppppp^^^^iiiiiiii^^^!!^^^^d^^dp^^!!^^ppdDDdddddpdddddddddppqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddDDddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqyyyyyyyyydddddddddddppppppppppdpddddppppppppgppppppppppphhhhhpppRrqqdddqdddddqqdqddddddddpprr*r^^^^^^!!!!!!^^^^!^^^^ppp^^^^^!^^!!^^^rrr^^!^!^^r^^^!^^^^^^^^^^^^!!!!!!!!!!^^^^^^^^pprpdddddddddddddddppppppppmmmmmmmmmmmmmmmmmmmmmmmmmppppppdddddddDDDdddddddddddrRdddddddddddddddrRRRRrddddddddddqlllllllllqdddDDDDDdddddqdddqllllllqddddddpppqqllqdddddddddqlqddddddddddddpppdppppppppiii^^iiiiiiiii^^^!^^^^^^^pp^^^^^ppddDDdddddddDdddpdppppqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddDDdddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqyyyyyyddddddddddddpppppddppppddpppgpppgpggggpppppppppphhpppppRRddddddddddddddddddddddddpp^^^^^^!^!^!^!^!!!^^!^^^pppp^^^^^!^^!!^^^^r^^^!^^^rrr^^!^^^^^^^^^^^^^!!!^^!!!!!!^^^^^iiirppdddddddddddddppdddpppmmpmmmmmmmmmmmmmmmmmmmmpmppppppdddddddDDDDdDDddddddddrRddddddddddddddddddddddddddddddddqlllllllllqdddDDDdddddddddqllllllllqddddddqqllllqddddDDddddqqddddddddpdppppppppppppppiiiiiiiiiiiiii^^^!!!!^^^^p^^^^ppppdddDDdddddDDdddddppppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqddDdDDddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqqqqqqqqddddddddpppppdddppppdpppppgggggggggppgppppphpphppppprRrdddddddddddddddddDDDddddd^^^^^^!!!!!^!^!!^^^^^^pppp^^^^^!!^!!^^^^rr^^^!!^^^rr^^^^^^^^^^^^^^^^^^!^^^^!!!!!^^^^^iriiddddddddddddddddddddpppppmmmmmmmmmmmmmmmmmmmpppmpppdddpddddddDDDDDDdddddddrRddddddddddddddddddddddddddddddddddqlllllllqddddDDDddddddqqdqlllllllllqddddddqlllllqqqddDDDdddddddddddddddpdpppppiiippiiiiiiiiiiiiii^^^^!!!^^^^pp^^^pppddpdDDDDdddDDDDdddpddpq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqdddDDDDddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssssssqqqqqqqqqpppdpdddpppppppggggggggggpggggppppppppppppppRRddddddddddddddddDDDddddd^^^^^!!!!!^!!^^^^^^^^^^^pp^^^!^^^^!!^^^^^r^^^^^^^^^r^^^^^^^^^^llll^^^^!^^^^!^!!!^^^^^^rriiidddddddddddddddddddddpppmmmppmmmmmmmmmmmmmppppmpppdddddddddDDDDDDDDdddddrRrdddddddddddddddddddddddddddddddddqlllllllllqdddDdDdddddqllqllllllllllqdddddqllllqllllqdDDDDddddddddddppdpddpdpppiiiipiiiiiiiiiiiii^^^!!!!^^^ppp^^ppppdpddDDdDDDDdDDDDddddqqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qddddDDDDDdddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssssssssqqddddddppppppgggggggggggggggpppppppppphhppprRRdddddddddddddDDDDDDDddd^^^^^^^!!!^!!^!!^^^^^^^pp^^^!!^^!^!!^^^^^^rr^^^^^rr^^^!^^^^lllllll^^^^^^^^^^^^^^!!^^^riiiiidiididddddddddddpddddpppmmppmmmmmmmmmmmmpppppppppdpdddddddDDDDDddDddddddRrddddddddDDddddddDDDdddddddddddddddqllllllqllqddddddddddqlllllllllllllllqddqqllllqdqlllqdDDDDDDDdddddddddddddddpppiiiipiiiiiiiiiii^^^^!!^^^^^ppppppppppdpdddddDDDDDDDdddddqsss~~~~~~~~~~~~~~~~sqqssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddDDDDDddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqdddddpddppppgggpppgggggggpppppppppppphhhppprRddppddddddddDddddDDDDddD^^^^^^!!!^^^^^^^^^^^^pp^^^!^^^^!^^!^^^^^^^rrr^^rr^^^!^^^llllllllll^^^^^^^^^^^^^^!^^r^^iiiiiiiiiiidddddddddddddddppmpppmmmmmmmmmmmmppppppdpdddddddddDDDDDDDDdDddddrRdddddddDDDDdddddddDDDDDddddddddddqqlllllqqdqqddddddddddddqlllllllllllllllqqlllllqdddqllqddDDDDDDddddddddppddddpppipiiiiiiiiiiii^^^^^^!!^^^ddddppdpppppppddddddddDDDDDddddqss~~~~~~~~~~~~~~~~sqqddqqqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qddddDDDDDDDdddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqdddddddpppdpppppgggggggppgppgggpppppphhppppRRrppdpppddDddddddDDDDDDDD^^^^!!!^^^^^^^^^^^^pp^^^^^^^!!!!!!^^^^^^^^^rr^^rr^^!^^^lllllllllll^^^^l^^^^^^^^^^^r^^^^iiiiiiiiiiddddddddddddddpppppmmmmmmmmmmmmppppppppdddddddddDddDDDDDDDdddddRrdddddDDDDDDDddddddDDDDdDDddddqqqqllllllqddddddddddDdddddddqlllllllllllllllllllqqqddddqqddddDDDdddddddgdpppppdppppippiiiiiiiii^^^^^^^!!!^^ddddddddpppdppqqqqddddddDDDDdddqss~~~~~~~~~~~~~~~sqqdddddddddqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddDDDddddddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddddddpppppddpggggggggppggggpppgpppphppppprRpdpppddddddddDDDDDDDDDDD^^^!!^^!^^^^^^^^^pppp^^^^^^^!!!!!^!^!^^^^^^rr^r^^!!!^^llllllllllllllllll^^^!^^^^^r^^^^iiiiiiiiiidpddddddddddddpppppmmmmmmmmmpmmpppppppdppdddddddddddDDDDDDddddrRdddddDDDDDDDDdddddDDDDDDDddddqlllllllllllqddddddddDDddddddddqqlllllllllllllllqqddppddpddddDDDDddddgddddggpppppppp^iiiiiiiiiiiiii^^^^^^^^^^ddddddddddppqqssssqqqqdddDDddddqss~~~~~~~~~~~~~~~qdpdddddddddddqs~~~~~~~~~~~~~~~~~~~~~~sqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddDDdddddddqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddddddddppdddppgpgggggppgggggppggppppppppprRdppppddddpdDDDDDDDDDDDDDD^^!!!^^^^^^^^^^ppppp^^!!^^!^!!!!!!!^!^^^^^^^rr^^!!!^lllllllllllllllllll^^^^^^^rr^^^^iiiiiiiiipdddddddddddddppppppmmmmmmmmmmppmpppppppppddddddddddDDdDDDDDdddrRrddddDDDDDDDDddddDDDDDDDDDdddddqlllllllllllqddddddDDDDDddddddddqlllllllllllllqdddddddddddddDDddddddddgdggpgpgpppp^^iiiiiiiiiiiiiiiii^^^^^^^ddDDDddddpppqsss~sssssqddDDddddqs~~~~~~~~~~~~~~~sqdddddpddddddddqqs~~~~~~~~~~~~s~~~~~~sqdqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqddddddddqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddpddddppppdddpppggggggggggggpgggppppppppppRddpppdpddddDDDDDDDDDDDDDD^^^!!^^^^^pp^^^ppp^^^!!^^!^!^!!!!!!!!^^!^^^^^r^^^^^^lllllllllllllllllll^^^^^^r^^^^^iiiiiiiipppppddpddddddddpppppmmmmmmmmmmpppppppdppppppppddddddddDDDDDDdddrRrdddddDDDDDDDdDddddDDDddDDDdddddqllllllllllllqdddddDDDDDDddddddqllllqqllllllllqdddddddddddddddddddddddgggggpggggpp^^^^^iiiiiiiiiiiiiiii^^^ddddDDDdddddppqs~ss~s~sssqdddddddqs~~~~~~~~~~~~~ssqdddddppddddddddddqs~~~~~~~~~~sqs~~~~sqdddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddddqqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddddddddddpppddpppppggggggggggggggppggppppppRdddppppddddddDDDDDDDDDDDD^^^^!!!^^^ppp^pppp^^^!^^!^^^^^!!!!!^!!^^^^^^^^rr^^^^lllllllllllllllllllll^^rr^^!^^iiiiiiiipppppppppdddddddddppmmmmmmmmmmmpppppppdddpppppppppddddddDdDDDDdddRrdddddddDDDDDDDDdddddDDDddDdddddqllllllllllllllqqqdddDDDDDddddqqllllqddqllllqqllqddDDdDdddddgddddgdgdddgggggggggpg^^^^^^^^iiiiii^^^iiiiiiiiiddDDDddpdpddqss~~~~~~~ssqdddddddq~~~~~~~~~~~sqqqqdddddddddddddddddddq~s~~~~~~~sqdqssssqddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddddddddppppppppppggggggggggggggggggpppprRdpppppdddddddDDDDDDDDDDDD^^^^!!!^^^^ppppppp^^!!^^^^^^!^!!!!!!^!^!!!^^^^^rr^^lllllllllllllllllllllllr^^^!!^^iiiiiiiiiipiippppppddddpdppmmmmmmmmmmmmppppppddddpdpppppdddddddddDDDDDddrRdddddddDdDDDDDDDDDddddDdddddddddqllllllllllqllllllqdddDDDDdddqlllllqdddqlllqddqqddDDDdDDdddggggdggggddggggggggggg^^^!!^^^^^^^^^^^^^^^^iidddddddDdddddpqqss~~~~~~~~~sqdddddqqs~~~~~~~~~ssqdddddddddddddddddddddqqss~~~~~~~ssqddqss~sqddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~ssssqssqdddddqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddddddddddppppggpggggggggggggggggggggpppRrpppppddddddddDDDDDDDDD^DDD^^^!!^^^^^ppppppp^^^^^^^^^^^^^^!!!!^^!^!!!^^^^^l^^lllllllllllllllllllllll^^^^!!^^iiiiiiiiiiiiiiipppddddpdppppppppmmmmmmpppppdpdddddpppppddddddddDDDDDDDddrRddddddDDDDDDDDDDDDDddddddddddddqllllllqqqqqdqqlllqdddddDDDddddqlllqddddqllqdddddddDDDDDdddggdggggggggdgggggggggg^^^!!!!!!^^^^^^!!!!^^^^i^dddddDDdddddqss~~~~~~~~~~~~sqqdddqs~~~~~~~~ssqqddddddddddddddddidddddddqs~~~~~~~~qdpdqs~~ssqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~sqqqqdqssqdddqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddddddddddddpppppgggggggggggggggggggggggrrrppppppddddddddDDDDDddDD^^DD^^^!^^^^^pppppppp^^^^pp^^^^^^^^!!!!!!^^!^!!^^^^llllllllllllllllllllllll^^^^!^^!^iiiiiiiiiipppppiippdddddpppdddpppmmmmmpppddppdddddppppdddpdddddDDDDDDDdddRrddddddDDDDDDDDDDDDdddddddddddddqlllllqddddqdddqlqdddddDDDDDddddqlqdddddqlrrddddddDDDDDdddddddddgggggggggggghhgg^^^!!^^!!!!!^^^^^!^!!!^^^^dddDDDddpddddqs~~~~~~~~~~~~~ssqddqs~~~~~~~sqqdqdddiiddddddiidiiiiddddddqss~~~~~~~sqddqss~s~ssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~sqdddddqsssqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddddddpdddppppggggggggggggggggggggggggrRppppppdddddddddDdDDDDddD^^^^^^^^^^^^^^ppppppppp^^pppp^^^^^^!^!!!!^^!^^^^^^^lllllllllllllllllllllllll^^^!!!!^^iiiiiiiiiiiiiiiiiippddddppdddppppmmmppppddddddddpddppppddddddddDdDDDDdddrRdddddDDdDDDDDDDDDDDDDddDddddddddqllllqddddddddqllqddddDDDDDDdddqllqddddddqRrddddddDDdDDddddddddgggggggggggghhhhg^^^^^^^^^!^^^^d^^^^^^^^dddddDDDDDddddddq~~~~~~~~~~~~~~~~sqq~~~~~~~~~qddddd^^^iiiidii^iii^^idddddddqsss~~~~~~sqqssqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~sqddddddqsssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqddddppdddppppggggggggggggqqqgggggggggrRrpppppppddpdddddddDDddddd^^^^^^!^^^^^^^pppppppppppp^^ppp^^^^^^^!!^^!^^^^^^^lllllllllllllllllllllllll^^^!!!!^^iiiiiiiiiiiiiiiiiiippddddppddpppppmppppddpdddddddddpdppppddddddDDDDDDDdddRrdddddDDDDDDDDDDDDDDDddDDdddddddddqlllqdddddddqlqqdddddDDDDDDddqllqddddddddRrdddDDdDDddddgdddddgggggggggggghhhgggg^^^^^gg^^^^^ddd^dd^^^dddddDDDddddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~ssqddddd^^^^^iiiiii^^^^^^^^dddddddqqqs~~~ssssssqdq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~qddDDDddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqddddppppppdppgggggggggqqsssqqgggggrrRRrpppppppppdddppddDDddddD^^^!^^!!^^^^^ppppppppppdpp^^^pppp^^^^^!!!^^^^^^lllllllllllllllllllllllllllll^^!!!^!^^^irrrrRRrriiiiiippppdppddpppppppppppppppddddddddddddddppppdddddDDDddddddrRrddddddDDDDDdDDDDdDDDDDDDDddddddddqllqdddddddddqddddddDDDDDDDdddqqddddpddddrRrdddDDDDddddggddgdggggggggggghhhhgggg^ggggggggggggddddddddddddddDDddddddddq~~~~~~~~~~~~~~~~~~~~~~~~~sqqqddd^^^^!!^^iiiiii^^^^^^^ddddddddddqs~sssqqqqdddq~~~~~~~~~~~~sqqss~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~sqdDDDdddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddppdddpdgggggqqqqqss~~ssqgqrrrRRRrpppppppppddddpdddddddddd^^^!!!^^^^^^ppppppppddddd^^^^^ppp^^^^^!!!!!^^^^llllllllllllllllllllllllllllll^^^!!!^^rRRRRRiRRRRRrpiiiipppdppdpdppppppppppdddddddddddddddddddpddddddDDddDddddRrddddddDDDDDDDDDdddDDDDDDddddDDdddddqrdddddddddddddddddDDDDDDDdddddddddddddddrRrddDDDDdddggggdgggggggggghhgghhhhgg^gggggggggg^^ggddddddddDDDDDDdddddddqq~~~~~~~sqq~~~~~~~~~~~~~ssqqppddd^^^!!!!^^^^iiiiiii^d^^^d^^dddddddqsssqdddddddq~~~~~~~~~~~sqddqqs~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~sqdDDdddqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqdppddpppdqqqqsssss~~~~~~sqsssRRRrpppppppppppppppddddddddddd^^^!!^^^ppppppppppdddddd^^^^^pppp^^^^^!!!^^^^^^^lllllllllllllllllllllllllllll^^^^^^rRR^iiiiiiiiRRrriiiiippppppphppppppppddddddddddddddddddddddddddddddddddrRddddddDDDDDDDdddddddddDDDdddddDDDddddrddddddddddddddddDDDDDDDDDDDddDddddDDddddrRrrddDDdddddggggggggggggghhhhggghgggggggggggggg^^^^dddddddDDDDDDdddqqqqqss~~~~~~sqddq~~~~~~~~~~~~sqpppddp^^!^!!^^^^^^^^^^^^^ddddd^^^ddddddqsssqddddddddq~~~~~~~~sssqdddddqs~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~qddDddddqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqpddddpdqssss~~~~~~~~~~~~ssssRRrrpppppppppppppppddddddddddd^^^^^^^dppppppddddddddddd^^dd^^pp^^^!!!!^^^^^^^^llllllllllllllllllllllllllllll^^^^^RR^^^^iiiiiirrRRrrrrrippppphhhphppppppddddddddddddddddddddddddddddddrRRRrdddddDDDDDDDdddddddddddDdddDDDDDdDdddrddddddddddddDDDDDDDDDDDDDDDDDDDDDDDDdddddrRrdddDdddggggggggggggggghgggggggggggggggggggggg^^^^ddDDDdDDDdddddqssss~~~~~~~ssqdddqs~~~~~~~~~~~qqppppp^^^^^^^^^^^^^^^^^^^^^^ddd^^ddddddqsssqddddddddqs~~~~~~ssqqqdddddddqs~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~sqqddddqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpddddddqsss~~~~~~~~~~~~~~~~~srrpppppppppddppppdpdddddddddddd^^^^ddpppppdddddddddddddddd^^^^^^^!!!!^^^^^^^llllllllllllllllllllllllllllllll^^^RR^^^^^iiiiiiiiirRRRRRrppppphhpphppppppddpddddddddddddddddddddddrRRRRRrrddddddDdDDDDDDDDDdDddddddddddDDDDDDDddddrddddddddddDDDDDDDDDDDDDDDDDDDDDDDDDDDDDddrRrrdDdddggdgggggggggggggggggggggggggggggggggggg^^ddDDDDDDDDddddqss~s~~~~~~~sqqqddddq~~~~~~~~~sqpppppppppppp^^^^*^^^^!^^^!^^^^dddDDDDddqssssqddddddddqs~~~~~sqqdddddd^dddqs~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~qdddddqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddqsss~~~~~~~~~~~~~~~~ssrqddpppppppdppdppppdddddddddddd^^^^dppppppdddddddDddddddd^^^^^^!^^!!!^^^^^^lllllllllllllllllllllllllllllllllllRRr^^^^^^^iiiiiiiiiiirrRRpppppppppppppppppdddddddrrrrrrrddddddddrRrrrddddddddddDDDDDDDDDDDDDdDdddddddDdDDDDDDddddrddddddddddddDDDDDdddDDDDDDDDDDDDDDDDDDDDDdrRRrrrdddgggggggggggggggdgggggggggggggggggggggddddddddDDDDdddqqss~~~~~~~~~~qdddddddqs~~~~~~~sqpppppppppppppppp^r^^!!!!!!!!^^^ddhDDDddqsqssssqddddpdqs~~~~~~qdddddddd^^ddqs~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~sqdddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~qdddddqqsssssss~~~~~~~~~~~~sqqqdddpdpddppppddpppdpddddddddddddp^^pppppppppdddDDDDDddddd^^^^^^!^!!!!!!^^^^ll^^^llllllllllllllllllllllllllllll^^^^^^!^^^^iiiiiiiiiiiirRRRpppppppppppppppppdddRRRRRRRRRRrdddddRRrdddddddDDdDDddDDDDDDDDDDDDDddDdddddddDDDDDDdddddrdddddddddddddDDdddddDDddDDDDDDDDDDDDDDDDDddrRRRRrggggggggggggggddddggggggggggggggggggdgggddddddDDDDddddqs~~~~~~~~~~qdddddddddq~~~~~~ssqpppppppppppppppprp^^^!!!!!!^^^ddhDDDDDDdqdqssssqddddqss~~~~~sqddddddd^^^^ddq~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~sqddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqqs~~~~~~~sqdddqsssssqqqqs~~~~~~~~~~sqddddddddpdddppddddpppppdddddddddpdpppppppppppddddDDDDDDdDd^^^!!!!!!^!^!^^^^^^^^^^^^lllllllllllllllllllllllllllll^^^^!!!^^^^ii^^iiiiiiiiirrRRrrrrppppppppppppddrRrddddddrrRRRRrRrrddddddddDDDDDDDDDDDDDDDDDDDDDdddddddddddDDdDDddppdrrddddddddpddddddddddDdddDDDDDDDDDDDDDDDDDddddrrRrggggggggdggdddddddgddggggggggggggqgqggggddddddddDdddqs~~~~~~~~~sqqdddddddddqs~~~~~~~sqpppppppppppppprppp^^!!^^^^^^^dDDDDDDDDddddqssqdddddqss~~~~ssqddd^^d^^^!^ddqs~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~sqddqs~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqdddqs~~~~~~~qdddqssssqddddqs~~~~~~~~~ssqdddpdddddddpdddddppppddddddddppppppppppppddpdddDDDDDDDddd^^^!!!^!!!!^!!!^^^^^^^^^^llllllllllllllllllllllllllllll^^^^!^^^^^^^^^^iiiiiiiiirrrRRRRrrpppppppppddrRrdddddddddddrrRrddddddDDdDdDDDDDDDDDDDddDDDDDDDddddddddddDDdddDddddpddrddddddddddddddddddddDDDDDDDDDDDDDDDDDDDddddddRrrgggggdddddddrrrddddddygyggggyggqsqsqggddqqqdddddddddq~~~~~~~~~qddddddddddqss~~~~~~~ssqppppppppppppprppp^^^!^^^^^dddDdDDDDDdddddqssqdddqqss~~~~ssqqdd^^^^^^!^^ddqs~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~sqddqs~~~sqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qdddddqss~~~~~~sqddqs~sqddddddqs~~~~~~~sqqdddddddddddddddddddppppdddddddpppppppppppppdddddDddDDDDDDd^^^!!!!^^^^!^!^^^^^^^^^^^^llllllllllllllllllllllllllllll^^^^!^^!!^^^^iiiii^iiiiiiirriRRrrrppppppprRRdddddddddddddddddddddDDDDdDDDDDDDDDDDDdDDDDDDDdDddddddddddddddddddddddddrdgdddddddddddddddddDdDDDDdDDDDDDDDDDDddddddddRrgddgdddddddrRRRrrdddyyyyyyyyyyqsssssqqdqssqddddddddq~~~~~~~~~~qddddddddqqss~~~~~~~~~~sqpppppppppppprpppp^^^^^dddddDDDDDDddddddqssssqqqss~s~~sqqqddd^^!!^^^^ddddqs~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~qqs~~ssqddqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qdddddqs~~~~~~~sqqs~~sqdddddddq~~~~~~sqdddddddddddddddddddddppppddddpppppphppppppppppdddDDddDDDDDDd^^^!!^^^^^^!^^^^^^^^^^^^^^llllllllllllllllllllllllllllllll^^^^^^!^^^iiiii^^iiiiiiiiiiiiRRrrppprRRRdddddddddddddddddddddDDDDDDDDDDDDDDDDDDDdDDDDDddDDdddpddddddddddddddddddddrggggdggdgddddddddddddDdDDddDDDDDDDDDDDdddddddrRddddddddddrRrddRrdddyyyyyyyyqqs~~~~sssqssssqqdddqqq~~~~~~~~~~~~qddqdqqqss~~~~~~~~~~~~~sqqppppppppprppppp^^^^^ppddDDDDDDDdddddqss~~ssss~~~~~sqddqddd^^!!!!!^^ddqs~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~qdddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddqs~~~~~~~ss~~~sqdddddddqs~~~~~~sqddddddddDdddddDddddppppppdddppphhppppppppppdddddDdddDDDDDDd^^!^!^^^^^^^^^^!!!!!^!!^^^llllllllllllllllllllllllllllllllll^^^^!!^^iiiii^^^iiiiiiiiiiiiRrrprRRrrddddddddddddddddddddddDDdDDDDDDDDDDDDDDDDDDDDDdDDddddddddddddddddddddddddddrgggdggggddddddpdddddddddDddDDDDDDDDDDDDddDDddrRrrdrrrrrrRRrdddrRrdyyyyrrrqq~~~~~~~~~~s~~ssssqqq~~~~~~~~~~~~~~~sqqsqsss~~~~~~~~~~~~~~~~sqppppppppprpppppp^^^^pdddDddddDDdddqqss~~~~s~~~~~ssqdddddddd^^^!!!^^^dqss~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~sqdddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddqs~~~~~~~~~~~sqdddddqqs~~~~~~ssqqdddddddDdDDDDDdddppppppppddpphhhhpppppgpppddddddddddDDDDd^^^!^!^^^l^^^^^^!!!!!!!!^^^llllllllllllllllllllllllllllllllll^^^^!^^^iiii^^^^^iiiiiiiiiiiiRRrrRpdddpddddddddddddDdddddddddDDDDDDDDDDDDDDDDDDDDDdddddddddddddddpddddddddddddddrgggggggggggdddddddddddddddDDDDDDDDDDDDDDdDDdddrRRRRRRRRRrrdddddrRrrrrRRRR~~~~~~ss~~~~~~~~~~ss~~~~~~~~~~~~~~~~~~ss~~~~~~~~~~~~~~~~~~~~sssqqqpppppprpppppp^^^dddDDdddddDDddqsss~~~~~~~~~~~sqddddd^^d^^^!!^!!^^ddqsss~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~sqddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddqs~~~~~~~~~~~sqdddddqs~~~~~~~~qdddddddDDdDDDDddddpppppppppppppphhhpppppggppppdddddddddDDDd^^^!!^^^lll^^^^^^!^!!^!!^^^^llllllllllllllllllllllllllllllllll^^^!!^^^ii^^!!^^iiiiiiiiiiiiiiRRrdddddddddddddddDDDDddddddddddDDDDDDDDDDDDdDdddDdddddpddddddddpddddddpdddddddddrggggggggggddddddpddpdpddddddDDDDDDDDDDDDDDDddddddddddddrdddddddddRRRRrrrdqqqqqsqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssqppppppprppppp^^^ddDDDdddddDdddqs~~~~~~~~~~~~sqddddd^^^^^^!!!!!!!^^ddqqs~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~sqdddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddqs~~~~~~~~~~~~sqdddqs~~~~~~s~sqdddddDDDDDDDdddddddppppppppppppppppppppggggpppddddddddddddd^^^^!^^llllll^^^^^^^^^!!!^^^lllllllllllllllllllllllllllllllllll^^^^^^^^^^^!!!^^^iiiiiiiiiiiiRrddddddddddddddDDDDDDDDdddddDDDDDDDDDDDDDDDDDddDDddddddddddddppppdddpdddddddddpddrgggggdgdggdddddpppppdddddddDDDDDDDDDDDDDDDDDddddddddddrddddDddddddddddddddyyyqyyq~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqs~s~sqppppppprppp^^^dddDDdddqddddqq~~~~~~~~~~~~ssqdddddd^!^^!^^^!!^^^^^ddddqss~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~qppddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddqs~~~~~~~~~~~~~sqqqs~~~~~~~ssqdddddDDDDDDDdddddpdppppppppppppppppppppgggggpppppddddppddddd^^^^^^^^llllq^^^^^^^^^^^^^^^lllllllllllllllllllllllllllllllllll^^!^^^^^^^^^^^^^^^iiiiiiii^iiRrddddddddddddddDDDDDDDDDDDDDDDDDDDDDDDDDddDddddddddpddddddddpppppddppppddddddddddrgggggddddggdpppppppppdddddddDDDDDDDDDDDDDDDDDDddddddddrdddDDDddddddddddddyyyyyyyyqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddqss~~sqqppppprpp^^^^dddddddqsqqqqs~~~~~~~~~~~~sqqqdddddd^^!!^^^^^!^^^^dddddqqqs~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~sqpppdpqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddqqs~~~~~~~~~~~~~ssssss~~~~~~~sqddddddDDDDDDDddddddppppppppppppppgppppppgggggppppdddddpdddddddd^^^^^lllllqiii^^^^^^^^^^^llllllllllllllllllllllllllllllllllll^^!!^^!^^^i^^^^^^^iiiiii^^^iiRrddddddddddddddddDDDDDDDDDDDDDDDDDDDDDDDDddddddddddddddddddpppppppppppppdddddddddrggggddddgggggpppppppppdddddddDDDdDDDDDDDDDDDDdddddddddrddDDDDDdddDdddddyyyyyyyyyyqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddqs~~~sqppppqsqpp^!^ddddddqsssss~~~~~~~~~~~~~sqddddd^i^^^^^^^^*^^!!^^dd^ddddddqs~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~qaaaappqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddqs~~~~~~~~~~~~~sqqqss~~~~~~~~sqdddDDDDDDDDDDdddpppppppggggppppppggppppgggggpgpppppddpppdddddddd^^^^^l^^llqqrrrrr^^^^^^^llllllllllllllllllllllllllllllllllll^^^!!^^^^^iiii^^^iiiiii^^^^iiRrdddddddddddddddddDDDDDDDDDDDDDDDDDDDDDDDdddddddddpdddddddpppppppppprrrrppddddrrrgggggddddgdgggpppddpppppdddddddDDddDDDD^^DDDdddddddddddrrdDDDDDDDDDdddyddyyyyyyyyyyqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qdddddq~~~~ssqqpqssqpp^!^^dddddqss~~~~~~~~~~~~~~sssqdddd^^ii^iiiidrR^^!!^d^^^^ddddddq~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~sqaaaaaaqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqs~~~~~~~~~~~~~sqdddqs~~~~~~~~ssqddDDDDDDDDDddddddpdppppgggggpppgggpppgggggpgggpppppppppdddddddd^^!!^^^lllllriiirrr^^rrrllllllllllllllllllllllllllllllllllll^^^!!^^^^^iiii^^^iiiiii^^^iiRrdddddddddddddddddDDDDDDDDDDDDDDDDDDDDDDDddddpddpdpdpdddddppppprppppppppprrrrrrgggggggddddddgggpppddddppdddddddddDddddDD^^^^^dddddddddddddrdDDDDDDDDDdddddddyyyyyyyyyyqssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddqs~~~~~ssqssqppp^^^dddqqqs~~~~~~~~~~~~~sqsssssqdd^^^^iiiiidrR^^!!^^^^^^dd^^dddqs~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~sqaaaaaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddqsss~~~~~~~sqddddDDDDDDDddddddddddpppggggggggggggpggggppgggppppppppppppdddddd^^^!!^^^llllqii^^^^rrrrllllllllllllllllllllllllllllllllllll^^^^!^^^^^^^^iiiiiiiiiiii^^irRrdddddddddddddddddDdDDDDDDDDDDDDDDDDDDDDddddddppppppppddddpppprppppppppppppppggggggggggddgddggpppdddddpddddddddddddddd^^^^^^^ddd^^ddddddddrdddDDDDDdDDdddddydddyyyyyyyqqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddq~~~~~~s~ssssqpddd^ddqsss~~~~~~~~~~~~~qqdqssssqd^^!!^iiiiddRr^^!!^^^^^^^d^^^^ddq~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~sqaaaaaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqssqqss~~~~sqdddddDDdDdDDDDdddddddpppppggggggggggggggggpggggpggppppppppppddppp^^!!!!!^^llqiii^^^^^^^^lllllllllllllllllllllllllllllllll^ll^^^!!!^^^^^^^iiiiiiiiiiiiiiiRRdddddddddddddddddddddDDDDDDDDDDDDDDDDDdDdddddpdppppppppddppppprppppppppppppppggggggggggggggggpppdpdddpppddddddddddddd^^^^^^dd^^^^^ydydddddrddddDDdddddddddddddddyyyyyyyyyyyqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddqq~~~~~~~~~~s~ssqddddddqss~~~~~~~~s~~~sqddddqqqqdd^!^^^iiidrRrp^^^!!^!!!^^^^!^^ddq~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~sqaaaaaaaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqddqs~~~~sqddddddDDdddDDdDDDddddppppppgggpgggggggggggggggggggggpppppppppppii^^^!!!^^^lllqii^^^^^^^^^^lllllllllllllllllllllllllllll^^^^^^^^!!^^!^^^^^^iiiiiiii^^iiiiRrdddddddddddddddddpdddddddDDDDDDDDDDDDDDdddddpddddpppppppppppprppppppppggpphhpppgghgggggggdddppppppddpppppdddddddddd^^^^!^dddd^^^ddyyyddddddrrdddddddddddddddddyyyyyyyyyyyyyyqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qddqqs~~~~~~~~~~~~~~sqdpdddqss~~~~~~~~sss~sqdddddddddd^^^^iiiddRRrd^^^^^!^!!^!!^^!!!^dqs~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~sqaaaaaaaaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddqs~~~sqddddddddddDDDDDDdddddpppppppgppgggggggggggggggggggggggpppddppppipii^^^!!^^llllqi^^^^^^^^^^^^lllllllllllllllllllllllllll^^^^^^^^^!!^!^^!^^^^^^^ii^^^^^iiiirRdddddddddddddddpdpddddddDDDdDDDDDDDDDDDDDdddddddpddppppppppprppppppppggggphhhppgggggggggggdddpppppppdpppdppdddddddd^^!!^^ddd^^^ddyyyyyydddddrddddddddddddddddyyyyyyyyyyyyyyyqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdqss~~~~~~~~~~~~~~~sqdddddqs~~~~~~~~sqssssqddddddddd^^^^iiiddRrdddiii^^^!!!!!^^^^^!^dqs~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~sqaaaaaaaaaaaq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddqs~~sqddddddddddddDDDDdddpppppppppppggggggggggggggggggggggppppddddppppiiii^^!^^llllll^^^^!!^^^^^^^^^llllllllllllllllllllllll^^^^^^^^^!!!!!!!^^^^^^^^iii^^^^^iiiiRddddddddddddddddpppdddddDdDDDDDDDDDDDDDDDdddddddddddpppppprrppppppppggggghhhpphhgggggggggggdggppppppppppppppdddddd^^!!^^dddddd^dyyyyyyyyyddddrddddddddrrrrrryyyyyyyyyyyyyyyqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qddqs~~~~~~~~qs~~~~~~~sqddddq~~~~~~~~~qdqqqqddddddddddi^^iidddrRdddddii^^^!^^!^^^i^^^^ddqs~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~sqaaaaaaaaaaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qdddq~~~~sqdddddqqdddddDDDDdddppppppppppppppgggggggggggggggggggppppddddpppiiiii^^^^lllll^^^^^!^!^^^^^^^^^llllllllllllllllllllll^^^^!^^^^^!!!!!!!^!^^^^^^iii^^^^^iiiirRdppdddddddddddddpdpdddDDDDDDDDDDDDDDDDDDDdddddddddddpppprpppppppppggghgghhgghhhgggggggggggggppppppppppppppppddddd^^!!^dddddpdddyyyyyyyyyyddddrddddddrrdddddryyyyyyyyyyyyqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqq~~~~~~~~sqdqs~~~~s~sqddddqss~~~~~~sqdddddddddddddddiiiiiddrRdddddii^^!!^^^^^^iii^^^ddqs~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~sqqaaaaaaaaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqs~~~~~sqqqqqssqqdddddDDdpddppdppppggpppggggggggggggggggggppppdddddddpppiiii^^^^llllll^^^^!^!^^^^^^^^^^^^^^llllllllllllllll^^^^^!^^^^!!^!!^^^!!^^!^^iiii^^^^iiiiirRddpddddddddddddddddddDdDDDDDDDDDDDDDDDDDDDddddddddddpprrpppppppppgggghhghggggggggggggggggggpppppppppppppddppdddd^^^^^^ddd^ddppyppyyyyyyyyddddrrrdrrrrdddddddryyyyyyyyyyqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqdddqs~~~~sssqddqss~~~~~sssqdddddddddddddhhdiidddRRddddddi^^^!^^^iiiiiiii^ddddq~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~ssqaaaaaaaajjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssss~ssqddddddddddddddppppggpppggggggggggggggggggppppdddddppppiiiiii^lllll^ll^^!^^!!!^!^^^^^^^^^^^^^^^llllllllll^^^^^^!^!!!!!!!!!!^!!!^^^^^^iiii^^^^iiiirRrdddddddddddddddddddDDDDdDDDDDDDDDDDDDDDdDDDddddddppprppppppppppppggggggggggggggggggggggpppppppppppppddpdpdddddddd^^^dd^^^dppdppypyyyyyyyyrrrddrrdddddddddddrryyyyyyyyyyqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqdddqss~~~~~sqddqs~~~ssqqsssqddddddddpddhhhhdddddRrdddddiii^^^^^iiiiiiiiiidddddq~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~sqjjjaaaaajjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddddpdddpppggggpggggggggggggggggggggppdddpppppppiiiiii^^lll^^^l^^^^!!!!!!^^^!^^^^^^^^^^^^llllllll^^^^^^^^!!^!^!!^^^^^^!!!^^^^^^^ii^^^^^^iiprRrdddddddddddddddddDDdddDDDDDDDDDDDDDDDDDDDDDddddddpprpppppppppppppppggggggggggggggpggpgpppppppppppdpdddppddddddddd^ddd^^^ddddddppppyyyrrrydddddddddddddddddyyryyyyyyyyyyyqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqddhddqs~~~~~ssqqs~~~~sqddqsqddddddDddddddhhdddddRrddddddiiii^^^^iiiii^^iddddddqs~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~sqjjaaaajjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqddddddddddpppgggggggggggggggggggggggggpppppppppppipiiiiiiqllll^^^^^^^^!!!!!^^!!^^^^^^^^^^^^^^^lll^^^^^^^!!^!^^^^^^^^^^^^!!!!!^^^^^i^^^^i^^iiiirRdddddddddddddddddddddddddDDDDDdDDDDDDDDDDdddddpddprpppppppppppppppppgggpggggggggggpgpppppppppppdppddddddddddddddddddd^^^dddddddpdprrryyyyydddddddddddddddyyyrryyyyyyyqqqsss~s~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqdddhhhddqss~~~s~ssss~sqqdddqqdddddDDdddddddddpddddRddddddddiiii^^iii^^^^^ddddddqs~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~sqjjaaajjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqddDdddddpppgggggggggggggggggggggggggppggpppppipiiiiiiiiiiRlll^^^^^^^!!!!!!!!!!^!^^^^!^!!^^^^^RRl^^^!!!!!!^^^^^^^!^!!^^^^^^!!^^^^^iiiiiiiiiiiiirRrdddddddddddddddddddddddDdDDDddDDDDDDddddddddddpprpppdddpppppppppppggpppgggggggpppppppppppppppppddddddddpdddddddddd^^^^dddddddpprppyyyyyyyyyyyddddddydyyyyyyrryyyyyyqssssssssqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qdddddhhhddqs~~~~~~s~sssqdddddddddddDDDddddpddppddpddRddddddddddii^iii^^^^^ddddddqss~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~sqjjjajjjjjjjqs~~~sqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddDDddddpppgggggggggggggggggggggggggppgggpppipiiiiiiiiiirRqql^^^^^^!!!^!!!!!^!!!^^^^!!!!!^^^^^RR^^^^!!!!^^^^^^^^^^^^^^^^^^!!^!!^^^^^^iiiiiiiiiirRdddddddpdddddddddddddddddddddddDDDDDDddddddddddrpppdddpdpppddppppppppppggggggggggpppppppppppddddddddddpddddddd^^dd^^^^^dddddpprppppyyyyyyyyyyyydddddyyyyyyyyrryyyyqsssss~sqqyyq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qddddDDdDhhdqss~~~~~~~ssqddddddddddDDDDDdddddpppppppppRddddddddddiiiii^^^!!^^dddddqs~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjjjjjqss~sqjq~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qddDDDDddppppppgggggggggggggggggggggpppgggggp^iiiiiiiiiiiiRrii^^^^^!!!!!!!!!!!^!^!^^!^^^!!!^^^vRRrv^^^^!!^^^^^^i^^^^^^^^^^!^^^^^!^^^^^^^iiiiiiiiiiRRddddddddddddddddddddddddddddddddDDDDdddddddddrppdppddddpdpdddppppppppggggggggggppppppppppddddddddddddddddddd^^^^^^^^^^ddddddrddddyyyyyyyyyyyyyddddyyyyyyyyyyrryyrrssssssqyyyyyqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qdddDDDDDDDddqsss~s~sssqdddddddddddDdDDddddddppppppppxrRpddddddddddiiiii^!!^^^dd^dqs~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjjjqssssqjjqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssqqqqs~~~~~~~~~~~~~sqddDDDddpppppppggggpgggggggggggggpggppggggg^^^iiiiiiiiiiiRrii^^^^^!!!!!!!!!!!!^!^^!^^^!!!^^^vvrRrvv^^^!^^^^^iii^^^^^^^^^^^^^^^!!!^^!^^^^^i^^^iiiiiRdddddddddddddddddddddddddddddddddDDDdddddddddrpddpddddddpdddppppppppppppgggggpggppppppmppppdddddddddddddddd^^^^^^!^^^^ddddddrdddddyyyyyyyyyyyyydyyyyyyyyyyyyyrrryyqqqqqqyyyyyyyqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddDDDDDDdddqqsssssssqddddddddDDDDDDDddddpppppppxpxSSRrddddddddddiiiii^^!!^^^^^dqqs~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjjjjqsssqjjjqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqppppqs~~~~~~~~~~~~sqdddDDdddpppppppgpgpgpgggggggggggpppppggg^^^^^iiiiiiiiiiiRrii^^!^^!!!!!!!!!!!^^^^^^^^^^^^^^^vvrRrvy^^^^^^^^iiiii^^^^ii^^^^^^^!^!!!!!!^^^^^^^^iiiiirRdddddddddddddddddddddddddddddddDDDDddddddddddrddddddddddpdppppppppppppppgpppppgpppppmmpppppdpdddddddddddddd^^^^!!^^drrddpdrdddddppyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddDDDDDDdddddqssqssssqdddddddDDDDDDDdddpdppppxxSSSSSSRddddddddddiiiii^^!!!!^^^dddq~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~ssqjjjjjjjqssssqjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppqpppppqs~~~~~~~~~~~sqddddddddpppppppppppppgggggggggpppppgppgg^^!!^iiiiiiiiiiRrriii^^^^^!!!!!^!!!^^^!^^^^^^^^^^vvvvRrvyy^^^^^^^iiiiiiiiiiiiiiii^^!!^!!^^^!^^^^^^^^^iiiiiiRrddddddpdddddddddddddddddddddddDDDDdddddddddrdddddddddddpppdppppppppppppppppppppppmmmmpppppddddddddddddddd^^!!^^rrrddrrrrdddddddppyyyyyydyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyqs~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqdpdddDdDDdddddqsqdqssssqpdddDDDDDdDDddddddpppppxSxSSSSRrdddddpddDiiiiii^^^^!!!^^^dq~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjjqsssqqjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqq~~~~~~~~~~~~~sqpppppppppqs~~~~~~~~~~~sqdddddddddppppppppgppgggggggggppgpggggggg^^^!^^iiiiiiiiiRriii^^^^^!!!!!!!^^^^^^^^^^^dd^^^^vvvRRvvyppd^^^^^iiiiiiiiiiiiiiii^^!!!^^^^^^^!^^!!^^^iiiiiirRRppddddddddddddddddddddddddDDDDDDdddddddddddrdddddddddddpddppppppppppppppppppppppmmmmmpppppdddddddddddd^^^^!!^^^^ddddddddddddddpppppyyddyyydyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyqs~~~~~~~~~~~~~~~~~~~~~~~~~~sqpdddddddddDddddqssqsssssqdddDDDDDDDdddddddddpppxSSSSSSSrRrddddddDDddiiir*^^^^!!^^^dq~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~ssqqqjjjqssqqjjjJJjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggqs~~~~~~~~~~~sqppppppppqs~~~~~~~~~~~~~sqqqdddddpppppppppggpggggggggggggggggggggg^^^^^^iiiiiiirRriii^^^!^!!^^!^^^^!^^^^^^^dddddddvvRrvvvydddd^^diiiiiiiiiiiiiiii^^^^^!^!^^^^^!!!!!!^^^iiiiiiiRrppddppdddddpddddddddddddDDDDDDDDDDddddddddrdddddddddpdddddppppppppppppppppppppmmmmmmmpppddddddpddddd^^^^!!!^^^^^^dddddddddddpppppppdddddddddyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyqs~~~~~~~~~~~~~~~~~~~~~~~~~qpppddppddddddddqssqssssssqddddDDDDDdddddddddpppxSSSSSSSSSrRdddrrrrddddrrii^ii^^^^^dqs~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~sssssqqqssqjjjjjJJjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqg^^gqs~~~~~~~~~~sqpppppppqs~~~~~~~~~~~~~~~sssqqpppppddppppgggpggggggggggggggggggggggg^!^^iirrRRRRriii^^^^^^!^^^^^^^^^^^^^^^^ddddddvRRrvyyyddddddddddiiiiiiiiiiiiii^^^^!^^!^^^^^^^^!!!!^^^iiiiippRRRRrrppdddppddddddddddddddDDDDDDDDDdddDddddrdddddddddddddppppppppppppppppppppmmmmmmmppppdddddppdddd^^^^!!!!!^^^^ddddddddddppppppppdddddddddyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyqss~~~~~~~~~~~~~~~~~~~~~~~~~sqpppppppdpdddddqsqdqsssqqqdddddDDDDdddpddddppppxSxSSSSSSSSRddrDDDDrrrrpiiiii^^^^^ddq~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~sqjjjjJJjjjqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqg^^^gqs~~~~~~~~~~~sqppppppqs~~~~~~~~~~~~~~~~~~ssqqppdddpppggggggggggggggggggggggggggg^^^^iirRRrriiiiiii^^!^!!^^^^^^^^^^^^^^ddddddddrRrvvyyddddddddddddiiiiiiiiiiiiii^^^^^^!^^vvv^^^^^^^^^ii^^^iidprrRRRrrppppddpdddddddddddddDDDDDDdDdddDDddddrdddddddddddddpppdpppppppppmmpmpmmpmmmmmmpppppdppppdddd^^^^!^^^^^^^ddddddddpdppppppphpdpddddddddydyyyyddyyyyyyyyyyyyyyyyyyyyyyyyyqss~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqppppddddddqssqddqsqdddddddDDDDDddddddpppppxxSSSSSSSSSSRrrddDDDDddddiiiiii^^^ddqs~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjjjJJJJjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgg^g^^ggq~~~~~~~~~~~sqpppppqs~~~~~~~~~~~~~~~~~~~~~ssqqqdddpgggggggggggggggggggggggggggg^^^irrRriiiiiiiii^^^^!^^^^^!!!^^^^^^^vddvddddRRrvvvyddddddddddddddiiiiiiiiiiiiii^^^!^^^^^vvv^^^^^^^^^^^^^^^ppdpddrRRRRrpppppdddddddddddDDDDDDDDDDDdDDddddrddddddddddddddpdddpdppppppmmmmpmpmmmmpmmppppppppppppdd^^^!^^^^^^^ddddddddddddpppphhhppddddddddddyydyddddyyyyyyyyyyyyyyyyyyyyyyddqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqppppddddqssssqqssqdddddDDDDDDDddddddppppppxSSxSSSSSSSRrdddDDDDDddiii^^ii^^dddqs~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjjJJJjJjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqg^^^^ggggqqs~~~~~~~~~~sqpppppqs~~~~~~~~~~~~~~~~~~~~~~sssqqqgggggggggggggggggggggggrrrggg^^irRRii^iiii^iiii^^^^^^^^!!!^^^^^^^vvvvRrRRRrvvvvyyddddDDddDdddddiiiiiiiiiiiiii^^^^!!^^^vvvvvv^^^^^^^^^^^^ddddddddpppRrpppppdddddddddDDDDDDDDDDDDDDDDdddrdddDDdddddddddppddpppppppmmmmmmmpmmmmpppppppmmppppppp^^^!!^^r^^ddddddddddddddpppphhhppddpddddddddyyddddddyddyyyyyyyyyyyyyyddyddddqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqpppddqsssqsssssqddddDDDDDDDDddddddpppppppxxSSSSSSSSRdddDDDDDdddii^^!^iidddqs~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjJjJJJJjjqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqgg^^^^gggggqs~~~~~~~~~~sqqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~ssqgggggggggggggggggggggqrrRRRrg^irRrii^^^^^^^iiiii^^^^^^!!!!^^vvvvvvvrRrRrrrvvvvyyyddddDDDDdddddddiiiiiiiiiiiiiii^^^!!^^^vvvvvvvv^^^!^!^^^^ddddpdddpprRppppddddddddddDDDDDDDDDDDDDDDDddqrdddDDDdddddddddppppppppppmpmmmmmmpmmppmpppmmmppppppppp^^!^^^^rrdddddddddddddpppppphppddpppddddddddddddddyydddyyyyyyyyyyyyyydddddddqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppqsssqdqqssqddddDDDDdDDDDDddddpdppppppxpSxSSSSSRrdddDDDDDDDdiii^^!^^ddqss~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjJJJJJjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqggg^^^!^ggggggqsss~~sss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqggggggggggggggggggggqqsRrprRRRRRiii^^^^^^^^^iiiiipi^^^^^^!^^vvvvvvrRrdddddvvyyyyddddDDDDDddddiiiiiiiiiiiiiiiiii^^^!!^^^vvvvvvvv^^!!!!!!^^^^ddddddddrRpppppddpdddddddDdDDDDDDDDdDDDdqqlrqDDDdDddddddddddppddppppppppmmmmmmmmpmmmmmpmmpppp^ppp^^^!!^^dddrddddddddddpppppppppppppppppddddddddddddddyydyyyyyyyyyyyyyddddddddddqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qpqssqqddddqsqddddDDDdDDDDddddddddppppppppxxSSSSrRdddddDDDDdDDdiii^^!^ddqs~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqjjJjJJJJjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqag^^^!!^^ggpgggqqqsssqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqgggggggggggggggggqss~sqpppprrrii^^^^^^^^^^^^iiiip^^^^^^^^^^vvvvrRrddddddvvydyyydddDDDdDdddddiiiddiiiiiiiiiiii^^^!!!!^^vvvvvvv^^^!!!!!!^^^dddddddprRrrpppppddddddddddDDDDDDDdddDdqlllllqDDDDddDdDddddpdddddppppppmmmmmmmmmmmmmmmmmmmmp^^^ppp^^^^^pddddrrpdddddppdppppppppppppppdpddddddpdddddddddyyyyddyydyyyyyyddddddddddqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qssqdddddqssqddddddDDDDddddddddddpppppppxpxSSSRRrdddddDDDDDDDdDiii^!^dqsss~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqjjj^^JJJJJjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqag^^^!!^^ggggpgpppqsqpppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqgggggggggggggggqss~ssqppppppiii^^^^^^!^^^^^iippp^^pp^^^^^^vvvvrRdddddvvvyyddyyddDDdDDDdddddiidddiiiiiiiiiiiii^^!!^^^^^vvvvvv^^^!!^!!^^^^dddddddddrhhrrppppddddddddddDDDDDDddqqqllllllqDqDDDdDDDDddddddddddppppmmmmmmmmmmmmmmmmmmmmm^^^^^ppp^^^pppdddpprpdddpppppppppppppppppdddpddddddddddddddddydddddddddyyyyddddddddddddqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqddqdqssqddddddddddddddddddddpppppppppppxSSRrdddddDDDDdDDDDDdii^^ddqsss~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjj^^^JJJJjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqaaa^!!!^^gggpgppppprpppppqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggggggggqqss~~ssqppppppppip^^^^^!!^^^^^^ipppppp^^^^^^vvvvrRdddvvvyyydddddddDdDDDDDdddiiiidddiiiiiiiiiiii^^^!^^^^^vvvvv^^^!!^^^^^^^ddddddddpdrhhhrpphdpppdddddddddDDDDDDqlllllllllqlqDDDDDDDDDddddddddddppmmmmmmmmmmmmmmmmmmmmm^^!^^pppp^pppdpppdprdpddpppppppppppppppppddddpdddddddpddddddddddddddddddyyddddDddddddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdqqsssqddpdddddddddpddddpdppppppppppppprRrddddDDDDddDDDDDDDdiiidpqsss~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~qqs~~~~~~~~~sqjjJJ^^JJJJjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjqqaa^!^^^ggggpppppprpppppppqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggqqqqqss~~~~ssqpppppppppppp^^^!!!^^^^^^ppppyy^^^^vvvvvvrRddvvyyyddddddddDDDDDDDDddddidiidiiiiiiiiiiiii^^^^^^^vvvvvv^^^!^^^^^^^iiddddddddphrrhhhrhhppdppdddddddDDDDDDddqlllllllllllqqqDDDDDDDDddddddddppmmmmmmmmmmmmmmmm^m^^^^^!!^^^pppppppppppprppppppppppppppppppppppdddpddddddddddDDdddddddDddddyyyddddDDddDddddddddqqss~ss~s~~~~~~~~~~~~sqs~~~~~~~~sssqssssssqqdddddqqddddddddddpdppppppppprrRpddddDDDDDddDDDDDDDiiiiipqsss~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~qjjss~~~~~~~~sqjjJJJJJJJJJjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjaa^^^^^^^^^ggpppprppppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggqssss~~~~~~~sqppppppppppppp^^!^!!^^^^ppppyyy^^^vvvvvvvRrvdvyyddddddddddDDDDDDDDddddddddiiiiiiiiiiiii^^^^^^^^^vvv^^^^!^!^^^iiiii^^^ddddddhhrrrhrhhhpppdddddddddDDDDddddqlllllllllllllqDDDDDDDdddddddppppmpmmmmmmmmmmmm^^^^!^^!!^^^^ppppppppppppprpppppppppppppppppppppppdppdddddddddDDDdDDddDDdddyddddDDDDDdDDDDDDddddddqqssqqqss~~~~~~~~~sqdqss~~~~~~~~sssqqsssssqdqqqssqddddddddddddppppppprRRppddddddDDddDDdDDDdDiii^^dpqs~~~~~~~~~~~~~
~~~~~~~~~~~~~~sssqjjjqs~~~~~~~sqjjjJJ^JJJJJJjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjjaaa^^^r^^^^ggggppprpppppppppppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qggggggqs~~~~~~~~~~~~sqpppppppp^ppp^^^!!!^^^^^pp^^^yyyyvvvvvvvRrvvvyddddddddddDdDDDDDDDDDddddddiiiiiiiiiiii^^^^^^!^^vvvv^^^^^^^iiiiiii^^^^^dddddddddrrRRrpppdddpddddddDDDDdddqllllllllllllllqDDDDDdddddddddpppppmmmmmmmmmmmm^^^^!!^!!^^^pppppppppppppppprrrppppppppppppppppppppppppdddddddddDDDDDDDDDdddddddDDDDDDDDDDDDdddddddddqqdddqs~~~~~~~~~sqddqs~~~~~~~s~sqddqqssssqsssssqddddddddddddpppppprRrppdddddddddddDddDDDddii^^^dddqs~~~~~~~~~~~~
~~~~~~~~~~~~~sqssqjjqss~~~~~~~sqjjJJ^^JJJJJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjaa^^^^r^^^aapppprppppppppppppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqggggqs~~~~~~~~~~~~sqppppppppp^^pp^^^!!!^^^^^^^^^^yyyyvvvvvvrRvvyydddddddDddDDDDDDDDDDDDddddddiiiiiiiiiiiii^^^!!^^vvvv^^^!!^^iiiiii^^^^^^^dddddddddddrrRrrddddddddddDDDDddddqllllllllllllllqDddDDdddddddppddppmmmmmmmmmmmm^^!^!!!!!^^^pp^^^ppppppppppppppprpppppppppppppppppppppppppppddddddDDDDDDDDdddddDDDDDDDDDDDDDDDddddddddddddddq~~~~~~~~~sqdddq~~~~~~~~sqdddddqssssssssssqddddddddddppppppRRrpppdpddddddddhdhdddDdddii^^ddddqs~~~~~~~~~~~
~~~~~~~~~~~~sqjqssqqss~~~~~~~~sqjjjj^^^JJJJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjj^^^^rr^^^aaarrrpppppppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqggqqs~~~~~~~~~~~~~~sqpppppppp^^^^^^^!!!!!^^^^^^^^^^yyvvvvvvRrvvyyyddddDDDDDDDDDDDDDDDDDDDDdddiiiiiiiiii^iii^^!^^^vvv^^^!!^^^^iiiii^^^^!!^^^ddddddddddrRRRrrdddddddDDDDdddddqllllllllllllllqdddDddddddpdpdddpppmmmmmmpmmmm^^^^^!!!!!^^^^^^^^iippppppppppppprppppppppppppppppppppppppppddpddddDDDDDDDDdDdDDDDDDDDDDDDDDDDDddDddddddddddqs~~~~~~~~~sqqdq~~~~~~~~ssqddddqsssssssssssqddddddddhpppppRrppppppdddpdddhhhddddDDddpiiidddddqs~~~~~~~~~~~
~~~~~~~~~~~sqqjjqssss~~~~~~~~~~~qjjj^^^^JJjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqjjjj^^jar^^^aaarapppppppppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqss~~~~~~~~~~~~~~~~sqppppppp^^^^^^^^!!^!!^^^^!^^^^^yvddvvrRvvvvyyydddDDDDDdDDDDDDDDDDDDdDdddiiiiiiii^^^^i^^^^!^^^vv^^^!!^^^iiiiii^^!!!^^^^ddpdddddddddrRRRRRrddddddDDddddqllllllllllllllllqqdddddddpppppdpppppmmmmpmmmm^^^p^^^!^!!^^!^!!!^^iipppppppppppprppppppppppppppppppppppppddpdddddddDDDDDDDDDDDDDDDDDDDDddDdDDDDDDDDDDddddddqs~~~~~~~~~~ssqs~~~~~~~ssqdddddqs~s~ssqqqsssqqddddddppppppRrppppppppddddhhhhddddDddddiddddddddqs~~~~~~~~~~
~~~~~~~~~~sqjjjjjqs~ssssss~~~~~~sqjjj^^^^JJjjjjqqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjJjjjjaaraaarraaaappppppppppppqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~~~~~~~~~~~~~~~~~~sqqpppppp^^^^^^!^!^!!!^^!!^^^^^^ddvdvrRrvvvvyydddDDDdDDDDDDDDDDDDDDDdddddiiiiiii^^^^^^^^^!^^^vvv^^!!^^iiiiiiii^^^!!!^^ddddddddddddddddrRRrdddddddddqqdqlllllllllllllllllqddddpddpppppppppmpmmpmmpmmm^ppp^^!!!!!!!!!^!!^ipppppppppppppprRpppppppppppppppppppppppdddddddddDdddDDDDdDDdddDDDDDdddDDDDDDDDDdDDDddddddqs~~~~~~~~~~s~~~~~~~~~~sqddddqss~~ssqdddqssssqddddpppppppRrppppppppphhphhhddddDDDdddddddDddddqs~~~~~~~~~~
~~~~~~~~~sqjJjJjjqsssqqqqss~~~~~~sqjjJ^^JJJjjjjjjqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjJjjjjjajrrraaaaaaapppppppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqppppp^^^^^!^^!^!!!!!!^!^^^^dddddvvRrvvvyyyydDDDDdDDdDDDDDDDDDDDdddddiiiiiii^^!!^^^^^!^^^^^^^^!!^^^iiiiiii^^^^!!!^^^ddddddddddddddddrRrddddddddqlqqllllllllllllllllqddddddddppdppppppppmpppppmppppppp^^!!^!!^^^^^^^iipppppppppppppRRrpppppppppppppppppppppppdpddddddDddddDDDddDddddDdDDdddddDDDDDDDDDDDdddddqs~~~~~~~~~ss~~~~~~~~~~sqdddqqss~~~sqddddqssssqdddddpppppppRqppppppppphpdphdddDDDDDDdddDDDddddqs~~~~~~~~~~
~~~~~~~~~sqjJJJJjjqsqjjjjqqs~~~~~sqjjjJJJJJjJJJjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjJjJJjjjjjraaaaaaapappppppppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqppppppp^^^^^^^!!!!!!!^!^^^dddddddvrRvvvyyydddDDddDDDDDDDDDDDDDddddiiiiiiiii^^^^^^!^^!^^^^^^^^!^^^^iiiiiii^^^^^!!!^^^ddddddddddddddddrRrddddddqlllllqqqlllllllllllqdddddaddppppppppppppppppppppppp^^p^^!!!!!^^ii^^iiipppppppppppprrRRrrpppppppppprRRrpppppppppddddddddddddDdddddpddDddddddddDDDDDDDDDDdDdddddqs~~~~~~~sqs~~~~~~~s~sqddddqss~s~ssqdddddqqssqdddddddppppqRsqqpppppppppddddddddDDddddddDDdddqs~~~~~~~~~~~
~~~~~~~~~~qjjJjJjjqsqjjjjjjqsss~~~sqjjjjjJJJJjJJJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjJJJJJJjjjjrraaaaaaaapqqppppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqppppppp^^^^^^^!!!!^!!^^^^ddddddvvvRrvvvyydddDDdddddDDDDDDDDDdddddiiiiiiiiii^^^^^^^!^^^^^^^^!^^^^^iiiiiiii^^^^^^!^^^dddddddddddddddddrRrrdddddqlqqqdddrllllllllqqddddddaaaaappppppppppppppaaaaap^^^pa^!!!!^^^^iiiiiipppppppppprrrpprRRRRrrpprRRRRRRRrpppppppppddddddddddddddddpppdpdddddddDddDDDDDDDDDDdddddq~~~~~~~~qdq~~~~~~ssssqdddqsss~~~ssqdddddddqssqqqddddppqpqssssqpppppppdddddddddddddddddDDDdddqs~~~~~~~~~~
~~~~~~~~~~qjjjjjjqssqjJJjjjjqqss~~sqjjjjJJJJJJJJJJjqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqjjJJJJJJjjjjjjraaaaaaaqsqppppppqppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppppppp^^^^^^!!!!!!!^^^^dddddddvvrRrvvyyddddDddddddDDDDDddddddiiiiiiiiiiiiii^^^!!!!!^!^^^!!!^^^^iiiiiiiiiii^^^^^^^^dddddddddddddddddrRRddddddqdddddrRlllllllqdddddddaaappapappppppppppaaaaaaaa^^^ap^^!!!^^^iiiiiipppppprrrrrrppppppprRRRRRRrppppppRrppppppddddddddddpdddpdppppppddppdddDDDDDDDDDDDDDddddddqs~~~~~~~sq~~~~~~qqqsssqddqss~~~~sqddddddddqqssssqdddpqsqssssssqqpppqpddddddddddddddddddDDDddqs~~~~~~~~~~
~~~~~~~~~~sqqqqqqs~sqjjJJjJjjjqs~~sqjjJJJJJJJJJJJJjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssqqjjjJJJjjJJJJjjjaraaaaaaaqssqppppqqppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppppppppp^^^^^^!!!^^^^^^^dddvdvvvvRrvyydddyddddddddDDDdDdddddiiiiiiiiiiiiii^^^^!!!!!^!!!^!!!!!^^iiiiiiiiiii^^^^^^^^^ddddddddpddpdddddrRrddddddrRRRRRrqqllrRrdddadddaaaaaaaaaaapaaapaapaaaaaaaap^paaa^^!!^^iiiiiipppppprrppppppppapppppprrrrppppphprRpppppppdpddddddppddddppppppppdddddddddDDDDDDDDDdddddddq~~~~~~~~~~~~~~~qqddqsssqddqss~~sqddddDddddddqqqssqqdpqsssss~sssqppqsqdddddddddddddpddddddddddqs~~~~~~~~~
~~~~~~~~~~~~sssss~~sqjjJJJJjjjqs~sqjjjJJjJJJJJJJJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqjjjjJJJJJJjJJJjjjjaraqaaaqssssqqqqssqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqppppppp^^ppp^^^^^!!^^^^^ddddddvvvvvRrvyyddddddpdpddddDDddddddiiiiiiiiiiiiiii^^^!^^!!!!!!!!!!!!!^^^^iiiiiiiiii^^i^^^^^^dpdddddpddddddddrRRrrrRRRRrrrrddddqqdrRrddaaaaaaaaaapaaaaapaaaaaaaaaaaaaaaaaaa^^^!!^^iiiiippppppprppppppaaapppppppppppppphhharRrppppppddppddpppppdddpppppppppdddddddDDDDDDDDDDDdddddqs~~~~~~~~~~~~~sqddddqsssqdqss~~sqdddddDDDdddddddqssqddqssqss~~sssqqsssqdpddddpddpppppddddddddddqs~~~~~~~~
~~~~~~~~~~~~~~~~~~~sqjjJJJjjjjq~~sqjjjJjjJJJJJJJJJJjqssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~~~~~~~~~~~~~sqjjjjjjjjjJJJJhhjJJjjjjarsqqqss~~~ssss~~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppppp^^^^^p^^^^^^!!^^^ddddddddvvvvRrvyyyyddddppddddddddddddiiiiiiiiiiiiiiii^!^^^^^!^^!!!!!^!!!^^^^^^iiiiiiiiiiiii^^^^dddpddpdpppdpddddrRRRRRrrrddddddddddddrRaadadaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa^^!!^^^iiiipppppprppppppaaaaaapaappapaapphhhaaaRrppppppppppdppppppppdppppppppddddddddDDDDDDDDDDDDdddqs~~~~~~~~~~~~~sqdddpddqsssqsss~ssqddddDDDDDdddddddqssqqssqdsss~~sssssssqdddddddpppppdppddddddddddqs~~~~~~~
~~~~~~~~~~~~~~~~~~sqjJJJJJjjjqs~~sqjjjjjjJJJJJJJJJJJjqqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqs~~~~~~~~~~~~~sqjJJjjjjjjJjhhhjjJJJJjjjqsssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqppppp^^^^^^^pppp^^^!!^^^dddddddddvvRrvvyyyydyypppdpddpdddpddiiiiiiiiiiiiiiii^^^^^^^^^^^!!^!!!!^!!^^^^^iiiiiiiiiiiiiiii^^ppddppppppppdddddrrdddddddddddddddddaarRaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa^!!!^^iirrrrppprrrpppppaaaaaaaaaaaaaahhhaahaaaaRRrppppppppppppppppppppppppppdddddddddDDDDDDDDDDDDDddqs~~~~~~~~~~~~~sqdddddddqssss~sssqdddDdDDDDDDDDddddqsssssqdddqs~~~~ssssqpppddddpppddddpdddddddddddqss~~~~~~
~~~~~~~~~~~~~~~~~sqjJJJJjJjjqs~~~sqjjjjjJJjJJJJjJJjJjjjjjqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqjjqs~~~~~~~~~~~~sqjjJjjqjjjjjhhjjqjJJJJjjjqssqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqppppp^^^!!!^^^pp^^!!!^^^^dddddddvvrRrvyyyyyyyyyppppppddddddppiiiiiiiiiiiiiiiii^^^^^^^^!!!^!^^^^^!!!^^^^^iiiiiiiiiiiiiiipppddppppppdpdpdddrddddddddddddddddddaarRaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa^!^^^^rriiirrrrppppppppaaaaaaaaaaaaaaahhaaaaaaaarRRrpprrppppppppppppppppppppdddddddDDDDDDDDDDDDddddddq~~~~~~~~~~~~~ssqqdddddqsssssssqqdddDDDDDDDDDddddqsssssqddddqss~sssssqpppppddpppddddpppdddddddddddqss~~~~~
~~~~~~~~~~~~~~~~~sqjJjJJjjjjqs~~sqjjjjjJJJJJJJJJJJJJjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~ssssqqqjjqs~~~~~~~~~~~~ssqjjjjqqjjjjjjjqsqjJJJJjjjqqjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqppppppp^^^!!!^^^p^^^^!^^^^dvdddyvvvRrvvyyyyyyyyyypyppppddpdpppiiiiiiiiiiiiiiiii^^^^^^^^^!!!^^^^^^!!^!^^^^iiiiiiiiiiiiiiippppp^^^ppppdddddrdddddddddddddddaddaaarRaaaaaaaaaaaaaaaaaaaaaaaaaaaajjajaaaaa^^^!^^rriiiiiaaaaappppppaaaaaaaaaaaaaaaaaaaaaaaaaarrRRRRRRppppppppppppppppppppdddddddDDDDDDDDdDddddddddq~~~~~~~~~~~~~sqppddddqsssssqqdddddDDDDDDDDDdddqsqqsqssqdddqsssssqqqpppppppddpppddddpppppdddddddddqss~~~~
~~~~~~~~~~~~~~~~~sqjjJJJjjjjqs~ssqjjjjj^JJJJJJJJJJJJJJjjqjqssss~~~~~~~~~~~~~~~~~~~~~~sqqqqqjjjjjqss~~~~~~~~~~~~~sqjjqsqjjjjjjqssqjJJJJJjjjjjjqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppppppp^^!!!^^^pp^^^!!^^ddddddyyvrRvvvvyyyyyyyyyyppphppppppddpiiiiiiiiiiiiiiii^i^^^^^^^^!!^^^^*^^!^!^^^^^iiiiiiiiiiiiiipppp^^^^ppppddpddrddddddddddddddddaaaaarRraaaaaaaaaaaaaaaaaaaaaaaaaajjaaaaaaa^^^!^^r^^^^iiiiaaaaappppaaaaaaaaaaaaaaaaaaaaaaaaaaaaarrraaRrppppppppppppppppppppppddddddDDDDDDDDddddqqqq~~~~~~~~~~~~~~~qppqqdqsssssqddddddDDDDDDDDDdddddqddqdqssqddqssssqpppppppgppppppdppddppppddddddddqqs~~~~~~
~~~~~~~~~~~~~~~~~sqjjJJJjjjqssssqjjjjjJ^^JJJJJJJJjjJJJjjjqssqqqs~~~~~~~~~~~~~~~~~~~~sqjjjjjjjjjjjqs~~~~~~sqqss~~ssqjq~~qqjjjqs~sqjjjjJJJjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqppppppp^^^!!^^pppp^^!!^^dddyyyyyrrRrvvvvyyyyyyyyyyphhhhpppddddiiiiiiiiiiiiiiiiiiiii^^^^^^^^^^rr^^!!!!!^^^^i^^^iiiiiiiiippppp^^^^pppppddrddddddddddddddddaaaaaaarRaaaaaaaaaaaaaaaaaaaaaaaaajjjjjjaaa^^^!!!^^^^^^^iiiaii^aappaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaRrppppppppppppppppppppppddddddDDDDdDDddddqsss~~~~~~~~~~~~~~~~sqqssqsssssqddddddDDDDDDDDdDDddpdddddddqsqdqssssqpppppppggpppppppppppppppddddddqqss~~~~~~~
~~~~~~~~~~~~~~~~~sqjjJJjqqqssssqjjjjjjJ^^JJJJJJJjjJjJJjjjjqqjjjqs~~~~~~~~~~~~~~~~~~sqjjjjjjjjjjjjqs~~~~~sqjjqs~~~~sqs~~~sqqqs~~~sqqqjjJJJjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqppppppp^^^!^^^ppp^^^^^^dddyyyvvrvrRRrvvvvvyyyyyyyyyhhppdddddpiiiiiiiiiiiiiiiiiiiiii^^^^^^^rrr^^!!!!!!!^^^^^^^^diiiiiipppppp^^^^^^pppddrdddddddddddddadddaaaaaarRaaaaaaaaaaaaaaaaaaaaaaaajajajjjjaa^^!!!^^^^!^^^iiiii^^aapaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaprRppppppppppppppppppppppddddddDddDdDdddddqs~~~~~~~~~~~~~~~~~~~~s~~s~qsssqdddddDDDDDDDddDDDDddddddddqqsqdqsssqppppppggggggpppppppppppppdddddqss~~~~~~~~~
~~~~~~~~~~~~~~~~~ssqjJJjqss~ssqjjjjjJ^^^^^JJJJJJJjJjjjjjjjjjjjjqs~~~~~~~~~~~~~~~sssqqjjjjjjJjJjjjqs~~~~sqqjjjqs~~~~~~~~~~sss~~~~~~~qjjjJjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppppp^^^!!^^ppp^^^^^^^dyvvrrrvvvrrRrvvvvyyyyyyyyyyppdddddpiiiiiiiiiiiiiiiiiiiiiiii^^^^^rr^r^^!!^!!!!!^^^^^^^^ppiiipppppppp^a^^^^pppprdddddddddddddddddaaaaaarrRraaaaaaaaaaaaaaaaaaaaaajjjjjjjjaa^^^^^^^!!^!^iiiii^^^aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaarRphpppppppppppppppppppddddddddddDDdddddqs~~~~~~~~~~~~~~~~~~~~~~~~~qpsssqddddddDDDDDDdDDDDDdddddddddqssqssssqpppppgggggggpgggppppppppddqqqqss~~~~~~~~~~
~~~~~~~~~~~~~~~~~ssqjjjjqs~~~~sqjjjjJ^^!^^JJJJJJJjJJjJJjjjjjjjjjqs~~~~~~~~~~~~sssqqjjjjJjjJJjjjjjjqs~~sqjjjjjqs~~~~~~~~~~~~~~~~~~~~~qjjjjjjqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqppppppp^^^^^^p^^^^^^^^^vrrvvvvvvvvrRRrvvvvyyyyyyyyppdddddpiiiiiiiiiiiiiiiiiiiiiiiii^^^rr^^rr^^!!!!!!^!^^!!^^^pppppppppppppaaaappppparddddddddddaaadddaaaaaaaaarRraaaaaaaaaaaaaaaggaaajjjjjJjjajaa^^^^a^^!!!^^^iii^^^aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaarRrhhrrRRRrpppppppppppddddddddddddddddddqs~~~~~~~~~~~~~~~~~~~~~~~~ssqs~ssqqdddDDDDDDDDDDdDdddddddddddqsssssssqqpppppggggggpgggpppppppqqssssss~~~~~~~~~~
~~~~~~~~~~~~~~~~~~sqjjjqs~~~~~~sqjjjJ^!!^^JJJJJJJJJJJJjjjjjjjjjjjqss~~~~~~~~ssqqqjjjjjJJJJJJJjjjjjqss~ssqqjjjjqs~~~~~~~~~~~~~~~~~~~~~qjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqppppppppp^^^^p^^^^^^^rrrvvvyyyyvvvvrrRrrvvvvvvvvyyyypddppiiiiipppppppiiiiiippiiiirrrrrr^^^^r^^^!!^!!!!!^!!^^^^pppppppappaaaaaaappaaaarddddadddaaaaadaaaaaaaaaaarRRaaaaaaaaaaaagaaaagjjjjjjJjjjjja^a^aaa^^^!!^^iii^^iaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaprRRRRRrprRrppppppppppppppdddddddddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~sssqddDdDdddDDDDddddddddddddddqss~ssssqppppppgggggggggggpgpgqsssssqqss~~~~~~~~~
~~~~~~~~~~~~~~~~~~sqjjjjqs~~~~~sqjjjj^^^^JJJJJJJJJJJJJJjjJjjJJjjjjqqss~~~~~sqqjjjjjjjJJJjJJJhhjjjjqs~~~sqjjJJjqs~~~~~~~~~~~~~~~~~~~~~~qjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqpppppppppp^^pp^^^^rr^^^^vyyyhhvyvvvvrRRRRrvvvvvyyyyppdppiiippppppppppiippppppppr^^^^^^^^^^r^^^^!^^!!!!!!^!^^^^^^^^ppppaaapaaaapaaaapardddddaaaaaaaaaaaaaaaaaaaaarRrraaaaaajajaagggggjjjJJJJjjjjagaajjjj^^!!!^^iiiiiaaaaaaaaajaaaaaaaaaaaaaaaaaaajaaaaaaaaaaarrrrapppRRpppppppppppppppddppddddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqdddddddDdDDdddddpddddddddddqs~~ssssqppqqqggggggggppgggggqssqqqddqqs~~~~~~~~
~~~~~~~~~~~~~~~~sqqjjjjjqss~~~~sqjjj^^^^JJjJJJJJJJJJJJJJJJJJjJjjjjjjqqs~~ssqjjjjjjjjJJJJJJJhhhjqqqs~~~~sqjjJJjjqs~~~~~~~~~~~~~~~~~~~~~~qqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqpppppppppppp^vrr^^^^^^yyyhhhhvvvvvvvvvrRRRrvvvvyyyppppiiipppppppppppppppppppr^^^^^^^^!!^rr^^^^^!!^^!!!!!!^^^^^^^aaaapaaaaaaaaaaaaaaaraddddaaaaaaaaaaaaaaaaaaaaarRRRraaajjaaajjggjjjjjJJJJjjjggaajjjjjj^^!!^^iiiiiiaaaaajaaajjjjjaaaaaaaaaaaajjjjaaaaaaaaaaaaaahppppRrpppppppppppppppddddddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddddddddDddhddddddddddddqss~~sqs~sqqsssqggggggppppgggqssqdddddddqs~~~~~~~
~~~~~~~~~~~~~~~sqjjjjjjjqs~~~~sqjjjj^^^JJjJhJJJJJJJJjJJjjJJJJJjjjjjjjjqssssqjjjjJJJjJJJJhJhhhjjqss~~~~sqjjJJJjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqppppppppvvvrv^^^^!^^^yyyyyyyyyvvvvvvvvvrrRvvvyyypppppiipppppppppqqqppqprrr^^^^^!^^!!!^^rr^^^!!^^^!^!!!!!^^^^^^^^aaaaaaaaaaaaaaaaaaraaaddaaaaaaaaaaaaaaajaaaaaajrrRRRRRRaajjjgjjjjJjJJJJjJjjjgjjjjjjgg^^^iiiiii^iiiaajjajjjjjjaaaaaaaaaaaaajjjjjaaaaaaaaaaaaaaappprRppppppppppppppppdpdddddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddddddhhhdddddddpddqss~~sqdqssss~ssqggpgggggpgggqssqddddddddqs~~~~~~~
~~~~~~~~~~~~~~~sqjjjjjjqss~~~sqqjjjJJJJJjjhhJJJJJJJJJJJJjjjJJJJjjjjjjqss~sqjjjjjJJJJJhJhhJJhhjjqqs~~~~sqjjjjJJjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssssqqqvpvvvvrrv^^^^!!^^^^^^^^^^vyyyyyvvvvvvvrRvvyyyppppppppppppppqqsssqqsrppppp^^^!!!!^!!^^r^^^^^^^^^!!!^^!!^!!^^^^^^aaaaaaaaaaaaaaaaaraaaaaaaaaaaaaaaaajjjggggjjjjjjrrrrrRrjjjjjgjjJJJJJJJJjjjjgjjJjjjg^^^iiiii^^iiiiaaajjjjjjjjaaaaaaaaaajjjjjjjaaaaaaaaaaaaaapapppRrrppppppppppppppddpdddqqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddddddddhhhhddddddddpqss~~sqddqss~~~~ssqgggqqqgggqqssqddddddddqs~~~~~~~~
~~~~~~~~~~~~~~~sqjjjjqqs~~~~sqjjjjjJJJJJjhhhJJJJJJJJJJJJJjjJJJJJjjjjjqs~~~sqjjjJJjJJJJJJJJJJjjjjjqs~~~~sqqjjJJJjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssssss~sssqvvvrrrvvv^^^^!!!^^^^^^^^^^yyyyyyyvvvvvrRrvvyyyyyppppppppppqss~sssssqpppppp^^!!!^^^^^^rr^^^^ppp^^^^!!!!^^!!^^^^^^^^aaaaaaaaaaaaaraaaaaaaaaaaaaaaaaajjjjggjjjjjjjjjjjjrRRrjjjjjjJJJJJJJJJjjjjjJJJjjj^^iiiiii^iii^iaajjjjjjjajaaaaaaaaaajjjjjjjajaaaaaaaaaaaaaaaparRRpppppppppppppppddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqddddphpdhhhhhdddddddddqsssssqdqsss~~~~sssqqqssqgggqssqdpdddddddq~~~~~~~~~
~~~~~~~~~~~~~~~sqjjjjqs~~~~~sqjjJjJJJJJJjjhhhJJJJJJJJJJJJjJJJjJjjjjqqs~~~~~sqjjjjjjjjJjjJJJjJjjjjqs~~~~sssqjJJjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssqqqqqqs~~~~sqvrvvvvvv^^!!!!!^!!!^^^^^^^yyyyyyyvyvvvrRrvvvyyyyppppppppqs~~~~ssqqpppppp^^!!^^^^^^^^^rr^^ppppp^^^^!!!!!!!!^^^^^^^^aaaaaaaaaaaaraaaaaaaaaaaaaaajaggjjjjjgjjJjjJJJjjjrrrRjjjjjJJJJJJJjJJJJJjjJJJjjjjjjji^^^^ii^^^ajjajjjjjjjjaaajjjjjaajjjjjjaaaaaaaaaaaaaaaapaaprRrpaaappppppppppdddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqddddpppphhhhhhpdddddqssqqsssqss~~~~~~~s~~~~~ssqgqssqppdddddddq~~~~~~~~~~
~~~~~~~~~~~~~~~sqjjjjqs~~~~sqjjJJj^^JJJJjjjhjJJJJJJJJJJJJJJJJjJjjjjqss~~~~~~sqqjjjjjjjjjjJjjjjjqqs~~~~~~sqjjJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqppppppqs~~~ssrvvvvpp^^^^!!!!!!^!!^!!!^^^^yyyyyyyyvvvvRrvvvyyyypppppppqs~~~~ssqppppppp^^^^^^^pp^^^pprpppppppp^^^^!!!!!!!!!!!^^^^aaaaaaagagaaraaaaaaaaaaaaaaagggjjjjjjjjjJJJJJJjjrrjrRrjjJJJjJJjJJJJJJJJJjJJJJJjjjjjj^!^^ii^^^aajaajajjjjjaajaajjjjaajjjjjjaaaaaaaaaaaaaaaaaapprRRrrrrppppppppppqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddppppphhhhhddddqssqddqssssssss~~~~~~~~~~~~sqssssqppdddddq~~~~~~~~~~~
~~~~~~~~~~~~~~~~sqqqqs~~~ssqjjJJJJ^^jjJjjjjjjjJJJJJjJJJJJJJJJJJjjjjqs~~~~~~~~ssqqqqqjjjjjjjjqqqss~~~~~~~sqjJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqppppppppppqs~~~~ssqvvppp^^^^!!^^!!^^^^!!^!^^^^yyyyyyyvvvvrRrpvyyypppppppqs~~~~~~~sqppppppp^^^^ppppppppprppppppppp^^^^^^^!!!!!^!!!^^^aaaagagggagraaaaaaaahhaaaaggggjjjjjjjjJJJJJjjjjrjjjrRrjjJJJJJJJJjjjJJjjJjJJJJjJJJj^^!^jii^!^^aaaaaaajjaajjajjjjjjjjjjjjjjjaaaaaaaaaaaaaaaaapaaarRRRRRRppppppqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qddddpppppppphpppddqssqddddqssssqqss~~~~~~~~~~~~~sqqssqqpdddq~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~sss~~~~sqqjjjjjJJ^^^jjjjjjjjjJJJJJJJJJJJJJJJJjjjjqs~~~~~~~~~~~~ssssqqqqjjjqsss~~~~~~~~~~qjjjqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppppppppppqs~~~~sqvppppp^^!!!^^^^^^^^^^!!!^^^^^^yyyyyyvvprRRvyyyyyyppqqs~~~~~~~~~sqqppppppppppppppppppprrppppppp^^^^^^^^!!!!!!^!^^^a^aggggggggraaaa^^^ahhhaajgjggjjJJjJJJjJJJjjrrrjjJjjrRRjjjJJJJjjjjjjjjjjJJJJJJJJJj^!!^jj^^!^^jaaaaaaaaajjjjjjjjjjjjjjjJjjjjjjaaaaaaaaaaaaaaaaaaaaaaaarRqqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddqqpppppppppphppqssqddddqssssqddqqs~~~~~~~~~~~sqddqssqddqq~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~qjjjJjjJJJ^^jjjjjrrrjjjJJJJJJJJJJJJJJJjjjjqs~~~~~~~~~~~~~~~~~sssqqqs~~~~~~~~~~~~~sqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppppppppppqs~~~~sqpppppp^^!!^^^^^pp^^pp^!!!!!^^^^^yyyyyyyvrRrpyyyyyppqs~~~~~~~~~~~sqppppppppppppppppppppprrrpppppp^^^^^^^^!^^!!^!^^^^^^^^^gggaraag^^^^^aaajajjjjgjJJJJJJJJjjjjrjjjjjJJjjrRRjjjJJjjjjjxjjjxjjjJJJJJJJJj^!^jj^!!^^aaaaaajjjjjjjjjjjjjjjjjjJJjjjjjaaaaaaaaaaaaaaaaaaaaaaaaaaRR~sss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqggpppppppphhppqsssqdddqssqqqddddqs~~~~~~~~~~sqdddqssqqs~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~sqjjJJJJJ^^^^jjjrjjjrjjjJJJJJJJJJJJJJJJJjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqppppppppppqs~~~~sqpppppp^!^!^^^pppppppp^^^^!^^^^^^yyyyyyyyrrrrrqqyypqs~~~~~~~~~~~~~sqqqqpppppppppppppppppppprppppppppp^^^^^^^!!!!^^^^^^^^^gggggrgg^^^^^^^^^^^^JjjjjJJJJjjjjxxrxxjjJJJJJjjrRRrjjjjjjxjjxxxjjjjjJjJJJJjj^^jj^^!!^^ajjaajjjjjjjjjjjjjjjjjjJJjjjjjjjjaaaaaaaaaaaaaaaaaaaaaaaaq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqgggpppppggpppqsssqppddqsqdddddddqs~~~~~~~~~sqddddqs~ss~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~sqjjJJJ^^^^^jrrjjjjjrjjJJJJJJJJJJJJJJJjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppppppppqs~~~~sqpppp^^^!^!^^pp^^pppppp^^^^pp^^ppppyyyyyrrsrsrssqqqss~~~~~~~~~~~~~~~sssqpppppppppppppppppppprppppppppp^^^^^^!!!!^!!^!!^^^gjjjjrggg^^^^^^^^^^^JJJjJJJjjjjxxSrxxxjjjJJJjjjjjrRjjjjxxjjxxxxxjxjjjjJJJJJjjjJJ^!!!^^jjjjjjjjjjjjjjjjjjjjjjjJJjjjjjjjjaaaaaaaaaaaaaaaaaaaaaaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggpgppppggppqs~ssqppqqssqdppdpdqs~~~~~~~~~sqdpddqs~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~sqjJJJJ^^^^^rjjjjjjjrjjjjJJJjJJJJJJJJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppppppqss~~~sqppppp^^!!!^^pp^^pppppppppppppppppppyyyyyrrrsssss~ss~~~~~~~~~~~~~~~~~~~sqppppppppppppppppppppprppppppppp^^^^^^^^!^^^^^!^^^^jgjjjrrgjg^^!!^!!^^JJJjJJjjxjxxSSrSSxxjjjjjjjxjxjRrrxxxjxxxxSSxxjjxjjjjjJJJJJJJ^!!!!^^jjjjjjjjjjjjjjJjJjjJjJJJJJjjjjjjaaaaaaaaaaaaaaaaaaaaaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qggggggppggggqss~~~sqqsssqqddpdddqs~~~~~~~~~sqdddqs~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~sqjJJJJ^^!!^*jjjJJjjjjrjjjjjJjjjJJjJJJjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppppqqs~~~~~sqpppp^^^!!!^^p^ppppppppppppppppppppyyyqyqrsssss~~s~~~~~~~~~~~~~~~~~~~~~~sqpppppppppppppppppppprrqppppppppp^^^^^^^^^^^^^^^^^^jjJjjjrjjj^^!!!^!!^^JJJJjjjjxSSxrSSxxxjxjjxjxxxSrRrSSSxxSxSSSxxxxxxjxxjjJJJJJJ^^^!!^^^jjJjjjjjjjjjJJJJjjjJJJJjJJjjjjjjgaaaaaaaaaaaaaaaaaaaqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggpgggggqs~~~~~ssssqdddddddqs~~~~~~~~~~sqdqq~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~ssqqjJJJJ^^!^^^jjjJjjJjjrjjjjjjjhjjJjJjJjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqppppqsss~~~~~sqppp^^!!^^^^^ppppppppppppppppppppppyyqsqssss~~s~~~~~~~~~~~~~~~~~~~~~~~~~ssqqpppppppppppppppppqsrsqppppppppppppp^^^^^ggg^^!^^^JJjjjrjjj^^^!!!!!^^^^JJJjxxSSSSrSSSSxxxxxxjxSSSSrRrSSSSSSSxSSxxSxxjjjxjjjJJJJJ^^^!!!^^JJJjJJjjjjJJJJJjJJJJJJJJJjjjjgaaaaaaaaaaaaaaaaaaaaaq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qggggggggggqs~~~~~~~sqdddddddqs~~~~~~~~~~~~sqss~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~qqjjJjJJJ^^!!^^JJjJJJJjjjrrjjhhjjjjjjjjjjjjqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqsss~~~~~sqpppp^^^^^^^^ppppppppppppppppppqpppppqssss~~~~~~~~~~~~~~~~~ss~~~~~~~~~~~~~~sqpppppppppppppppqqssssqppppppppppppaaaaagggg^^!!^^^JJjjjrjj^^^^^^^^!^^^^JJjxSSSSSrSSxSSxxxSxxSxSSSSrRRRrSSSSSSSSSxxxxxxjjjjjJJJJJ^^!!!^^JJJJJJJJjjJJJJJJJJJJJjjJjjjjjgggaaaaaaaaaaaaaaaaaqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggggq~~~~~~~ssqdddddddqs~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~qjjjJjjJJ^^^!!^^JJJJJJJJjjjjrjjhhjjjjjjjjjjqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssssssss~~sqpppp^^^^^pppppppppppppppppppqq~qqppqss~~~~~~~~~~~~~~~~~~~sqqss~~~~~~~~~~~~~sqqqppppppppppppqs~~sqppppppppppppppaaaagjggj^^!!!^^^^jjrjJJ^^^^^^^!!^^^^^^xxxxSSrSSSSSxSxxxxSSSSxSSSSrRRrSSSSSSSxxSxxSxjxjjjJJJJJJ!!!^JJJJJJJJJJJJJJJJJJJJJJjjjjjjjgjgggaaaaaaaaaaaaaaaqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqggggggggqss~~~~~~sqpddpdddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~qjjJJJJJJ^^^!!^^JJJJJJJJjjjjrjjjjjjjjjjjjjqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~sssqqqss~sqpppp^^pppppppppppppppppppppq~~~~~qq~~~~~~~~~~~~~~~~~~~~~sqaaqqqsss~~~~~~~~~~sssqqpppppppqqqs~~~sqppppppppppppaaaaaggjjjj^^^!!!^^^jjrjjJJJJJJJ^^!!!!^^jjjxSSSrSSSSSSxSSSxSSSSSxSSSSrRRrrSSSSSSSxSxxxxxjjJJjJJJJ^!!^JJJJJJJJJJJJJJJJJJJJJJJjJJjjjjgggjgaaaaaaaaaaaaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqggggggqs~~~~~~~~sqpppdddddqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~sqqjJjJJ^^^!^!^JJJJJJJJJJjjjjrrjjjjjjjjrrrssqsss~~~~~~~~~~~~~~~~~~sssssqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppqssqpppppppppppppppppppppppppqqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqaaaaaqqqqss~~~~~~~~~~sqpppppppqss~~~~~sqpppppppppppaaagjgjjjjjj^^^^^^^^^jrjjjJJJjJJJ^^!^^^^^jxSSSSrSSSSSSSSxxSxxSSSSSSSSSSrRRRrSSSxSSSSxxxxxjxjJJJJ^^!^^^JJJJJJJJJJJJJJJJJJJJJJJJJjjjjjggggggaaaaaaajaaaq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggqs~~~~~~~sqppppdddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~sqjJJJJ^^^!^!^^JJJJJJJJJJjjjjjrrrrrrrrjjqsqjqqqs~~~~~~~~~~~~~~~~sqqqqqjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppqsssqpppppppppppppppppppppppqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qaaaaaaaaaaqqqs~~~~~~~~~sqpppppqs~~~~~~~sqppppppppppppaqqjjjgjjJJJ^^^^^^^JjjrjjjjjjJJJj^^^^jjjxxxSSSSrSSSSSxxxjjxxxSSSSSSSSSrrrRrrSSSSSSSSSxSxjjjjjJJ^^!!^^JJJJJJJJJJJJJJJJJJJJJJJJJJjjjjjjgggjgjaajjjjaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggqqss~~~~~~~qppppqqdddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~sqjJJJJ^^!!!^^^JJJJJJJJJjJJjjJjjjjjjjjjjjqjjjjjqs~~~~~~~~~~~~~~sqjjjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~sqppppqss~sqqqqppppppppppppppppppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqaaaaaaaaaaaaaqs~~~~~~~~ssqqpppqs~~~~~~~~qppppppppppaaqssqjjjjJJJ^^^^JJJJJJjjrjjjjjjjJJ^jjjjxxxxSSSSrrSSSSSxjjjjjjxjxSSSSSSrSSSrRRSSSSSSSSxSxjjjjjJJJJ^^!^^JJ^JJJJJJJJJJJJJJJJJJJJJJjjjjjjjjjjjjjjajjjjaqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qgggqqss~~~~~~~~~~qqppqsqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~qjjjJJJ^^!^!!^^^^JJJJJJJJJJjJJjjjjjjjjjjjjjjjjjjqs~~~~~~~~~~~~sqjjjjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqssqpppppqss~~ssssqppppppppppppqpppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qaaaaaaaaaaaaaaqsss~qqqsssssqqqs~~~~~~~~~sqqpppppppaaaaqssqjjJJJJJJJJJJjJJjjjrjjqjjjjjjjjjxjxxSxSSSrSrSSSxxSxjjjjjjjSSSSSSSrSSSSSrRSSSSSSSSxxxxjjjjjjjj^^^JJ^^JJJJJJJJJJJJJJJJJJJJJJJjJjjjjgjjjjjjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqss~~~~~~~~~~~~ssqqsssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~sqjJJJJJ^!!^^!^^^^JJJjJJJJJJJJJJjjJjjjjjJJjjJjjjqs~~~~~~~~~~~~~sqjjjjJJJJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppqsqppppppqs~~~~sqppppppppppppq~qqpq~~~~~~~ss~~~~~~~~~~~~~~~~~~~~~~~~ssqaaaaaaaaaaaaaqqqqqjjjqs~sssss~~~~~~~~~~~ssqpppppaaaaaaqsqjjjJJJJJJJjjJJJjjjjrqsqqqjjjjjjxxSxxSSSrSSrSSxxjxjjjjjjjxxSSSSSrSSSSSSSRrSSSSSSSxSxjjxjjjjjjjj^jj^^^^JJJJJJjJJjJJJJJJJJJJJJJJjjjjjjjjjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~sqjjJJJJJJ^^!!!^^^^JJjJJJjJJJJJJJJJJJjjJJjJJJJjjjjqs~~~~~~~~~~~~sqjJJJjJJjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppqsqppppppqs~~~~~sqpppppppppqq~~~~q~~~~~ssqqqs~~~~~~~~~~~~~~~~~~~~~~~~~sqaaaaaaaaajaajjjjjjjjqss~~~~~~~~~~~~~~~~~~qppppppaaaapqsqjjjjJJJJJJjjjjjjjjqrsssssqqjjxxxxSSSSSrSSSSrSSxxjjjjjjjxSSSSSrrSSSSSSSSrRrSSSSSSSxxxjjjxjjjjjjjj^^!!^JJJJjJJjjjJJJJJjJJJJJJjjJjjjjjjjjjjjjjjqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~sqjjJJJJJ^^^^!!^!!^JJJJJjJJJjJJJJJJJJJJJJJJJJJJjjjqs~~~~~~~~~~ssqjjJJJJJjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqppqs~sqpppppqs~~~~~~sqpppqppppq~~~~~~~~~~~sqaaaq~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqaaaaaaajjjJJJJJjjqs~~~~~~~~~~~~~~~~~~~sqppppqqaaqqsssqjjjjJJjJjjjjjjjjqssss~~~ssqjjxSSSSSSrSSSSSSrSSxxjjjjxxSSSSSrSSSSSSSSSSSrRSSSSSxSSSSxjjxjxjjjjjjjj^^^jJJJjjjjjjJJJJjjJJJJJJJjJjjJJjjjjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~sqjjJjJJ^^^^^!!!!^JJJJJJJJJJJJJJJJJJJJJJJJJJJJjjjjqss~~~~~~~ssqjjjJjJJJjjjjqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqs~~~sqqpppqs~~~~~~~~qqq~qqqq~~~~~~~~~~~sqaaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~sssqaaaajjjjjJJJjjjqss~~~~~~~~~~~~~~~~~~~~sqqpqssqqss~~sqjjjJJjjjjjjjjjjqs~ss~~~~~~sqxSSSSSSSrSSSSSSSrSxxjjjxxSSSSrrSSSSSSSSSSSSrRSSSSSSSSxSxxxjjjjxjjj^jjjj^jjJjjjjjjjjJJjjjJJJJJJJJJJJJJJJjjjjgjgjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~sqjjJJJJJJ^^!!!^^JjJJJJJJJJJJJJJJJJJJJJJJJJJJJjjjqqqsssss~~ssqjjjjJjJjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~~~~ssqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqaaaaqss~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqajjjjJJJJJjjqqs~~~~~~~~~~~~~~~~~~~~~~~ssqs~~ss~~~~ssqjjjjjjjjjjjqqqs~~~~~~~~~~~sqSSssSsrSSSSSSSSrSSSxjxSSSSrrSSSSSSSSSSSSSSSRrrSSSSSSSSSSSxxxxjjjj^^^jjjjjjjjjjjjjjjjjjJJJJJJJJJJJJJJjJjjjjgggjjqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqdddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~sqjjJJJJJJ^^^!^^JJJJJJJJJJJJJJJJJJJJJJJJJJJJjjjjjjqsqssqsssqqjjjJJJjjjjjqss~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqjJjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqaaaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjjjjJJJJJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~sqjjjjjjjqqqss~~~~~~~~~~~~~ssssssssssSSSSSSrSSSSjjSSSSrSSSSSSSSSSSSSSSSSSRrSSSSSSSSSxSSSSxxjj^^!^^jjjjjjjjjjjjjjjJJJJJJJJJJJJJJJJJJjjjgjgjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~sqjJJJJJJJ^!^^^JJJJJJJJJJJJJJJJJJJJJJJjJJJJjjJjjjrqjqqjqqqjjjjjJJjjjqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqaaaq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjjjjjJjjjjjqs~~~~~sss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqjjjqqsss~~~~~~~~~~~~~~~~~~ss~ssssssSSSSrSSSSSxSSSSrSSSSSSSSSSSSSSSSSSRrSSSSSSSSSSSxSxxxjj^!^^^jjjjjjjjjjjjjjjjJJJJJJJJJJJJJJJJJjjjjjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qddqddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~sqjjjJJJJJ^^^^JJJJJJJJJJJJJJJJJJJJJJJJjJJJJJJJjjrqjjjjjjjjjjjjjJJJjjjqss~~~~~~~~sss~~~~~~~~~~~~~~~~~sqjjjJjqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~ss~~~~~~~~~~~~~~~~~~~~~~ssqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqjjjjqjjjqs~~~ssqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqjjqss~~~~~~~~~~~~~~~~~~~s~~~s~sssssrrrSSSSSSSSSSrSSSSSSSSSSSSSSSSSSSrRSSSSSSSSSSSSSSSxjj^^!^jjjqqqqqjjjjjjjjjjJJJJJJJJJJJJJJJJjjjjjjjjhhjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqsqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~sqjJJJJJj^^^^JJJJJJJJJJJJJjJjJJJJJJJjjJJJJjjjjjrjjjjjjjjjjjjjJJJJjjjjqss~~~~~ssqqqs~~~~~~~~~~~~~~~~sqjjjJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqssqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqjjqsqqqs~~~sqqjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqs~~~~~~~~~~~~~~~~~~~~~~~~s~~~~s~ssrSSSSSSSSSSSrSSSSSSSSSSSSSSSSSSSrRSSSSSSSSSSSSSSxSxjj^!!^qqsssssqqqqjjjjjjJJJjjJJJJJJjjJJJjjjjjjjjhhjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqqjjjqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~sqjJJjjJJJ^^^JJJJJJJJJJJJJJJJJJJjjjjjJJjjjjjjrrjjjjjjjjjjjJjJJJJJjjjjjqs~~~~sqqjjjqs~~~~~~~~~~~~~~sqjjJJJJjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqaaaqqaaqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqs~~ss~~~sqjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssSSSSSSSSSSSrSSSSSSSSSSSSSSSSSSSSrRSSSSSSSSSSSxSSSxxj^^!^sss~~~~sssqjjjjjjjjjjJJJJJJJjjjJjjjjjjjhjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqjjjjjjjjqqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~sqjjJJjJJjJJJJJJJJJJJJJJJJJjJJJJJjjjjjjjjjjrrjjjjjjjjJJjjJJJjJJJJjjjjjqss~~sqjjjjjjqss~~~~~~~~~~~~sqjjJJJJjJjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqaaaaaaaaaaq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~sssSsSSSSSSSrSSSSSSSSSSSSSSSSSSSSSSRRSSSSSSSSSSSSSSxqqs^^^ss~~~~~~~~sqjjjjjjjjjJJJJJJJjjjjjjjjjhhhhjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqjjjjjjjjjjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~qjjJJjjJJJJJJJJJJJJJJJJJJJJJJJjjjrjjjjjjjrrjjjjjjjjJJJJJjJJJJJJJjjjjgqssssqgjjjJjjjqqs~~~~~~~~~~~sqjjJjJJJJjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqaaaaaaaaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssSSsSSSrSSSSSSSSSSSSSSSSSSSSSSSrrRrSSSSSSSSSSSxjqsss^^s~~~~~~~~~~sqjjjjjjjjJjJJJJJJjjjjjhjjhhhjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqjjjjjjjjjjjjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjJJJJJJJJJJJJJJJJJJJJJJjjjjrrjjjjrjjjjjjJJJJJJJJjJJJJJJJJjjjgjgqqqqgjjjJJJjjjjq~~~~~~~~~~~sqjjJJJJJJjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjjaaaaaaaaabs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssssssssSrrSSSSSSSSSSSSSSSSSSSSSSSSrRRrrrsSSSSSSxxqs~~~ss~~~~~~~~~~~~~qqjjjjjjjJJJJJjjJjjjhhjhhhhjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qssqqqjjjjjjjjjJjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjJjJJJJJJJJJJJJJJJJJJJJJJjjjjjrjjrgjjjjjJJJJJJJJjjJJJjJJJJjjgjgggggggggjJJJjjjjjqs~~~~~~~~sqjjJJJjJJJJjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjaaaaaaaaaabs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssssssrsSSSSSSSSSSSSSSSSSSSSSSSSSrRRrssssSSsSsss~~~~~~~~~~~~~~~~~~~sqjjjjjjjJJJJJJjjjjjhjjhhjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjqqjjjjjjjjjjjjJJjJjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqjjjjjjJJJJJJJJJJJJJJJJjJJJjjjjjjrrgjjjjjjJJJjJJJJJJJJJJJJjJjjjjjgggggggjjJjjjxxxqss~~~~~~~sqjjjJJjJJJJJjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjJjjjaaaaaaaaabss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~sssssssSSSSSSSSSSSSSSSSsSSSSSSrrRsssssssssss~~~~~~~~~~~~~~~~~~~~sqjjjjjjjjjJjJJjjjjjjjhhjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjjjjjjjjjjJJJJjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjj^^^JJJ^JJJJJJJJJJJJJJjjjJjjjjrjjjjjJJJJJJJJJJJJjjjJjjjjjjgjjggggggjJJjjxxSSrrss~~~s~sqqgjjjjjJJJJJjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjJJjjjjaaaaaaabss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~sqaaq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~sssssssSSSSSSSsSSSSsssSSSSSSSSrsssssssssss~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjjjjjJJJjjjjjjjjjjjjqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjjjjjjJjjJJjJjJjJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjJJJ^^^^^^^^JJJJJJJjJJJJJJJjjjjjrgjjjjjjJJJJjJJJJJjjjjjjjjjjjjjggggjgjjjjxxSSSrqssssssssSxgggjjjJjJJJjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjjjJjjjjaaaaaabss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqsqqaaaq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssssSsSSSSSSsSSsssssSSSSSssssss~ss~~s~~~~~~~~~~~~~~~~~~~~~~~~~qjjjjjjjjjjjjJjjjjjjjjjjqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjjjjjjJjJJjJJJJJJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjJJ^^^^^^^^^JJJJJjjJJJJJJJJJJjjjrjjjjjjJjJjjjJJJJjjjjjjjjjjjjjggggggjjjjxSSSrSSqssssqrqSxxgggjjJjJjJjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjJJJjjjjaaabss~~sss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqaaaqaaaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~sssssssSSssssssssssssSSSssssss~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqjjjjjjjjjjjjjjjjjjjqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjjjjjjjjjjJJJJJJJjJJJjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjJJJJJ^^^^^^JJJJjjjJJJJJJJJJjjjjrggjjjjJJjjjjjJJjjjjjjjjjjjjgggggggjjjjxxxSrSSSxqssqSrrSSxgxjjjjjJJjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqjJJJJJjjaaabssssqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~sqaaaaaaaaabsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssssssss~ss~~ss~ssssss~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjjjjjjjjjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjjjjJjJJJJJJJJjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjJJJJ^^!^^^jJJjjjJJjjjjjjjjjjjrgjjjjjjjjjjjjjJjjjjjjajggjgggggggjjjjjxSSSrSSSSqrsqSSrSSxxgggjjjJjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjJJJjjjaaabssqqjjjqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqssqaaaaaaaaabbbbss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~s~~~~~~~~~~sss~s~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjjjjjjjjjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqjjjjjjjjjjJJJJJJJJJJJjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjJjJJJJ^^^!^^^jjjjjJjjjjjjjjjjjrjjjjjjjjjjjjjjjjjjjjaaaagggggggggggjjjxxxxSrSSSSrqqSSSrSSSSxggjjjJjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjJJJjjjjjbbssqjjjJjjbbs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqaaqqaaaaaaaaaaaaabbss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjqqqjjjjjjjjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqjjjjjjjjjjjJJJJJJJJjjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjjjjjj^^!^^^jjjjjjjjjjjjjjjjrjjjjjjjaajjjajjjjjjjjaaaaagggggggggjjjjjjxxSrSSSSrSSxSSrSSxSSxgjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjJjJJjjqsssssqjjJjjjbabs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~sqaaaaaaaaaaaaaaaaaajqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqsssqjjjjjqjjjjjjqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjjjjjjjjjjjjJJjJJJJJJjjjjjjjqss~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjjjjjjjjjja^^!^^^jjjjjjjjjjgjjrrrjjjjjaaaaaaaaajjjjjjaaaaaaaaagggggggggjjjjjxSSrSSrSSSSSrSSSSSxxxgjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjjJJJjjqsssqjjjjjjjaaabs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~~~sss~~~~~~~~~~~qqqsssqaahaaaaaaaaaaaaaaajjjqqqs~~~~~~~~~~~~~~~~~sqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~sqjjjqsqqjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqjjjjjjjjjjjJJJJJJJJJJJJjjjjjjrsss~~~~ssqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqjjjjjjjja^^!!!^jjjjjjjjjgrrrjjjjjjggjjaaaaaaaajajjjjaaaaaaaggggggggjggjjjjxSSSrSrSSSSrrSSSSxSSxggjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqjJJJjqqsssqjjJJjaaaaabs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqsqqqqss~~~~~~~sqjjjqqqaahhhaaaaaaaaaaaaaajjjjjjqqs~~~~~~~~~~~~~~sqjjqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjqsssqqjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~sqqjjjjjjjjjjJJJJJJJJJJJJJJJjjjjjrqqqssssqqjqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqjjjjjjjaa^^!!!^gjjjjrrrrrrjjjjjgjggjjjaaaaaaaaajjjaaaaaaaaggaagggggggggjjxxSSSSrrSSrrSSSSSSSSSxxgjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjJJjjjqsssqjjJjjaaaaabs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjqjjjjqqs~~~~~sqjjjjjjaaahhhhaaaaaaaaajaajjjjjjjjjqs~~~~~~~~~~~ssqjjjjjqqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjqs~~~ssqjjjqs~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjjJJjjjJJJJJJJJJJJJJJJJjjjrjjjjqqqqjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqjjaaa^^!!^^gjjjrrjrrjjjjjjjjjgjjjaaaaaaaaaaaaaaaaaaahaaaaaagggggggggxxxxSSSSrrrSSSSSSxxxxxxggggq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjqs~ssqjjjjjaaaabs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjjJjjjjjjjjq~~~~~sqjjjJjjajaahhhaaaaaaaajjjaajjJJjjjjjqs~~~~~~~~~sqqjjJJJjjjqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~q~~~~~~~sqqqs~~~~~~~~~~~~~~~~~~~~~~~~qqjjjjjjJJJjjjjJJJJJJJJJJJJJJJjjjjrjjjjjjjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqqj^^^^!!^^rrrrjjjjrjjjjjjjjgggaaaaaabbbbaaabbaaaahhhhaahaaggggggggggxxSxSSSrrSSSSSSxxxaaaaaggqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjqss~~sqjJJjjaaaaabs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqjJJjjjjjjjqs~~~~sqjjJJjjjjjahhhaaaaaaajjjjajjjJJjJjjjqs~~~~~~~~sqjjjjjJJJjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~~~~~~~~~~~~~~~~~~~~~~~qjjjjjjjJJJJJjjJJJJJJJJJJJJJJJJjjjjrjjjjjjjjjjjjjjjqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss^^^^^!!!^^jjjjjjjrrjjjgjgggagaaaaabllllbabllbaahhhhaahhhggggggggggggxSSSSrSSSSSSSxxxaaajjjagqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjjqs~~~~~qjjJjjaaaaabs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjJJjjjqqqsss~~sqjjjJJjjjjjaaaaaaaaaaajjjaaajjJJJJJjjjqs~~~~~~sqjjJJjJJJJJJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjjjjjjjjJJJJJJJJJJJJJJJJJJJjJjjjrrjjjjjjjjjjjjjjjjjjqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s^^^!!!^^^^jjjjjjjjrrjjgggggaaaaabbllllllbllllbaahhaaahhgagggggggggrrrrrrrSSSSSSxxxxaaajjjaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqqs~~~~sqjjJJjaaaaabs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjqssssssssqqjjJJJJJjjjaahaaaaaaaaajjaaaajjjJJJjjjjqssss~~sqjjJJJJJJJJJJJjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjjjjjJJJJJJJJJJJJJJJJjJjjjrjjjjjhjjjjJJjjjjjjjjjjqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss^^^!!^!^^^^jjjggjjjrrgggggggaaabllllllllllllllbqahaaqaaphgggggSrrSSgggxxxSSxSSxggaaajjjjjjaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjJJJjjjqbbss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjqssssqqqqjjjjJJJJjjaaaaaaaaaaaaaajjjjajjJjJJJjjjjqqqqsssssqjjjJJjJJjJjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqjjjjjjjjJJJJJJJJJJJJJJJJJJJjjrjjhhjjjjjJJJJjjjjjjjjjjjjqqqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss^^!!^^!!^^^jggggggaarrggggaaaqbllllllllllllllllqaaqqlqgaggggSSSrSSgggggxxxxSSxxxgaaaajjjjjaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjjJJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqqssqqqjjjjjjjjJJJJjjjaaaaaaaaaaaaaajjjjjJJJJJJJJjjjjjjqssssqjjjjjjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqjjjjjjjJJJJJJJJJJJJJJJJJJjrjjhhhjjjjJJJJJjjjjjjjjjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss^^^!!!^!!!^^^^ggjgaaaaargggggarlllllllllllllllllllqqllllqqqgggSrrSSSggggggxgxxxxxgggaaaajjjjjaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqjjjjjqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssssqjjjjjjjjjJJJJJjjjjjaaaaaaaaaaaajjJJjJJJJJJJJJJJJJjjjqssssqqqqqqqjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqjjjjjjjJjJJJJJJJJJJJJJJJrJjjjhjjjjJJjJJjjjjjjjjjjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss^^^!!!!^^!^!^^^^ggggaaaarrggarrrqlllllllllllllllllllllllllllrrrrrSSSgggggggggggxgggggagaaaajjaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjJJjJJJJJJJjjaajaaaaaaaaaaajjjjJJJJJJJJJJJJJJJjjjqss~~~ssssssqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjjJJJJJJJJJJJJJJJrrJJJJjjJJJjJJJJJJjJjjJJjjjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss^^!!^!!^^^!!^^^^gggggaaagrggrrgggqlllllllllllllllllllllllllqddddSSSSdgggggggggggggggggaaaaajaaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqsssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjjJJJJJJJjJJjJJjjjajjaaaaaaaaaaajjjJJJJjJJJJJJJJJjjjjqs~~~~~~~~~~ssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqjjjjjjJjJJJJJJJJJJJJJrJJJJJJjjjJJjJJJJJJJJjjjjjjjjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss^^!!!!!!^!!^^^^^ggggagaggrrrrgggqlllllllllllllllllllllllllqddddgddddgddggggggggggggggaagaaaaaaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqqqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjjJJJJJjjjJJjjJJJjjjjaaaaaaaaajaajjjJJjJJJJJJjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjJJJJJJJJJJJJJJJrJJJJJJJJjJJJJJJJJJJJJjjJJjjjjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss^^^^^^!^!!!!^^^^^^gggggagggggggggqlllllllllllllllllllllllllqddddddddddddgggggggggggggggggggaaaaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqjjjJJjjajjjjjjjjjjjaaaaaaaajjjjjjJJJJJJJJJJjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjjJJJJJJJJJJJJJJJrJJJJJJJJJJJJJJJJjjJjJJJJjjjjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss^^^!^^^^^^!!^^^^gggggggggggggggggqlllllllllllllqlllllllllqqddddddDDDDddddgggggggggggggggggggaaaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqjjjJjjaajjaajjjjjjaaaaaaajjjjjjJJJjJJJjJJjjjjjqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjjJJJJJJJJJJJJJJJJrJJJJJJJJJJJJJJJJJjJJjJJJJJjjjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~sssss~~~s^^^!!^^^^^^!!^^^gggggggggggggggggggqllllllllllqqdqlllllllqdddddDdDDdDDDddddgggggggggggggggggggaapqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjJJJJjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjjjjjaajaaaaajjjaaaaaabbjjjjjJJJJJJJjjjjjjqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjjjjJJjJJJJJJJJJJJJrJJJJJJJJJJJJJJJJJJJJJJJjjjjjjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~ss^^^sssss^^!!^^^r^^^!!^^gggggggggggggggggggggqllllllllqdddqllllllllqDdddDDdDDDDDdddgggggggggggggggggggggaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqjJJJJjjqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjaaaaaaaajjjaaaaabbsssqqqjjjJJJJjjjjjqqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqjjjjjjjjjJJjjJJJJJJJJJJJrJJJJJJJJJJJJJJJJJJJJJJJJjJjJjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~ss^^^sss^^^^!!^^^^r^^!!^^^ggggggggggggggggggggggqlllllllqddddqlllllllqdDDDDDDdDDDdddggggggggggggggggggggggaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqjjJJJJJjjqssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qaajjaaaaaaaaaaaaaaaabsss~sssqjjjjJjjjjqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqjjjjqssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqqjjjjjjjgjjjjjJJJJJJJJJJJrJJJJJJJJJJJJJJJJJJJJJJJJJJjjJjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~ss^^^^ss^^^^!!^^^irr^^!!^^^ggggggggggggggggggdddgqlllllqqqddddqllllqqlqdddddDDDDDDddgggddggggggggggggggggqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqjjJjJjJJjqsssqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqaaaaaaaaaaaaaaaaaaabsss~~~~sqjjjjjjjqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjJjjjqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqaaqqjjjjjjjjjjJjJjJJjjJJJJJrJJJJJJJJJJJJJJJJJJJJJJJJJJJJJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~ss^^^^^s^^^^!!^^^rr^^^!^^^pgggpgpppggpggggggdddddgqqqqqddddDdddqllqddrrddddDDDdDDDddgddddggggggggggggggggqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjJJjjjjjqssqjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqaaaaaaaaaaaaaaaaaabsss~~~~~~sqqqqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjJJjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqaaaaajjggjjjjjgjjjjjjjjJJJJJJrJJJJJJJJJJJJJJJJJJJJJJJJJJJJJjrrrss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~ss^^^^^^^^^^!!^^^^ri^^!^^^^ppgggppgpppggggggggddDdddddddDDddDddddqqdddddrrddDDDDDDDddddddgggggggggggggggggqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~ssqjjJJjjqqqsssqjjqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqaaaaaaaaaqaaaaaqqss~~~~~~~~~~ssssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjJJJJJJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqaaaaaaajgjgjjgjjjjjjjjjjJJJJJJJrJJJJJJJJJJJJJJJJJJJJJJJJJJJJJrjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~s^^^^!^^^^^^!!^^^irri^^!^^^ppppgppppppppppgpddddDDDDddddDDDDDDDdddddddddddrdddDDDDDDdddddgggggggggggggggggqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqssssqqjjjqssssqqjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqaaaqaaqqsqaaaqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqs~~~~~~~~qjjJJjJJJjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqs~~~~~~qaaaaaaaaggjjggjjjjjjjjjJJJJJJJJJJrJJJJJJJJJJJJJJJJJJJJJJJJJJJrJjjjqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~^^^^^^!!^!!!!!!!^^iirii^^!^^^pppppppppppppppppdddddDDddDDDDDDDDDDDDdDddDdDddrddddDdDDDDddggggggggggggqqqgggqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjqqssssqjqss~sqjjjjjjjqss~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqsqqss~sqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjqs~~~~~~~qjjJjJJJJjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssqaqs~~~ssqaaaaaaagggggggggjjjjjjjjjJJJJJJJJJrJJJJJJJJJJJJJJJJJJJJJJJJrrJJjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~^^^^!!!!!!!^!!^^^iri^^^!!^^ppp^ppppppppppppppppddddddddDDDDDDdDDDDDDDDDDDddrdddDDDDDdDddggggggggggqqsssqqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~sqjjjjjjqssssqs~~sqqjjjJJjjjqssqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~ss~~~~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjqs~~~~~~~sqjjJJJJjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqqqaaqsssssqqaaaaaagg^^gggggggjjjJjjJJJJJJJJJJJJrJJJJJJJJJJJJJJJJJJJJJrrJJJJjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~ss^^^!!!!!!!!^^^irr^^^^!^^ppp^^pppppppppppppppppdpddpdddDDDDDDDDDDDDDDDDdddrdddDdDDddddgggpgggggggqss~~ss~~~~~~~~~~~~qs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqssssqqjjqqss~~ss~~sqjjjjJJJjjjqqqjqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjq~~~~~~~sqjjjJJJjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqaaaaaaaaaqqqqqaaaaaaa^^^^^^^^ggjjjjjJjJJJJJJJJJJJJJrJJJJJJJJJJJJJJJJJJJJrJJJJJJjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~s^^^^!!^!!!!!^^^iri^^^^^^^ppp^^ppppppppppwppppppppppddddddDdDDDDDDDDDDDdddrrddDDdDdddddpppggggggqqs~~~~~~~~~~~~~~~~sqjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjqsssssqqsss~~~~~~sqjjjjjJJJjJjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssssqjJjjqs~~~~~~~sqjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqqppppqqss~~sss~~~~~~~~~~~~~~~~~~~~sqqqqaaaaaaaaaaaaaaaaaaaaa^^^^!!^^ggggjjjjjjJJJJJJJJJJhhJJrJJJJJJhhJJJJJJJJJJJrJJJJJjjjjjjqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~ss^^^!!!!!!!^^^^^rri^^!!^^^pp^^^ppppppppppppppwpwppppdpdddddDDdDDDDDDDDdddrrddDDDDDddpdpppppgggggqs~~~~~~~~~~~~~~~ssqjjjqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqj^^jqss~~ss~~~~~~~~ssqjjjJJJJJJJjjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqssqqjJJjjjqss~~~~~~qjjjjqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqpppppppppqqsssssss~~~~~~~ss~~~~~~~~sqaaaaaaa^^aaaaaaaaaaaaaaa^^^^!!!^^jgjjjjjjJJJJJJJJJJhhhhJJrJJJJhJhhJJJJJJJJJJJrJJJJjjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~sss^^!!!!!!!!^^^^iri^^^!^^^pp^^^^^pwppppwpwpppppwwpppppddddpdddddddDDDDDddrrdddDDDDDDddpppppgggggqs~~~~~~~~~~~~~~sqqqjjjjjqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjj^^^jjqss~~~~~~~~~~sqqjjJjJJJjJJJJjJJjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjqqqjjjJJJjjjqss~~~~~sqqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~sqqqqpppppppp^pppp^s^^^^sss~sssss~~~s~~~~sqaaaaaaa^^^^aa^^aaaaaaaaaa^^^^^^^^jjjjjjJjJJJJJJJJJJJJJhhhJrJJhhhhJJJJJJJJJJJJrJJJJjJJJjJJjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~ss^^^!!!!!!!^^^^^rri^^^!^^^^pp^^^^pppwpppppwpppwwwwpppppppppddddddddDDDdddrrddDDDddDDddddppgggggggqs~~~~~~~~~~~~sqjjjjJJjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqj^^^jjqss~~~~~~~~~~sqjjjJJJJjjjjjJJJJJJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~s~~~~~~~~~~~~qjjjjjjjJjJJJjjjqqs~~~ssssss~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqqsqppppppppppp^^ppp^^^^^^^^^sss^^^^ssss~sssqaaaaaaa^^^^^^^^^^aaaaaaaaaa^^^r^jjjjjjjjJjJJJJJJJJJJJJJJhhJrJhhhhJJJJJJJJJJJJrrJJJJJJJJJJJjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~ss^^^^^!!!^!!^^^irii^^^!!^^^pp^^^^ppppwwwppppppppwwppppppppppdddppddDDDDdddrddddDdddDDdddppppgggggqs~~~~~~~~~~~~qjjjjjJJJJjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjj^^^jjjqss~~~~~~~ssqjjjjJJJjjjjjjjJJjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqssqsss~sss~~~~sqjjjJJJJJJJJJJjjjjqs~ssssss~~~~~~~~~~~~~~~~~~~~~~~~sssqqqpppqpppppppppp^^^pppp^^^^^^^^^^^^^^^^^^sssss^aaaaaaa^^^^^^^^^^^^^^^aaaa^^^^^rrrjjjjjjjjjjJJJJJJJJJJJJJJJJrJJhhJJJJJrrrrrrrrJJJJJJJJJJJJjjjjjjqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~ss^^^!!!!^^^^^iirii^^^!!^^^^p^^^pppwwwwpwwpppppwpppppppwppppdpppddddddDDdddrrddddpddDdddpppppggggqs~~~~~~~~~~~sqjjJJJJJJJJJjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjjjjjjqqs~~~~~~~~~sqqjjJJJjjjqqqqjjJjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqssssqqqpqqpqqqsqqqs~~~sqjjjjJJJJJJJJjjjqqsssssssqs~~~~~~~~~~~~~~~~~~~~~~ssqqqpppppppppppppp^^^^^^pp^^^^^^^^^^^^^^^!!^^^^sss^^^aaa^^^^^^!!^^!!!^^^^^^^^^^^^^^^jjrrjjjjjjjjjJJJJJJJJJJJJrrrrJJJJJJJrrJJJJJJJJJJJJJJJJJJJjJjjjjjjqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~ss^^!!!^^^^iiii*iii^^!!!^^^ppp^^pwpwwwwwwpwppwpppppppppppppppppppddddddddddrrddddpdddpdpppppggggqs~~~~~~s~~~~sqjjjJJjjJjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqjjqqqsss~~~~~~~~sqjjjjjjjjjqssssqjjjjqqqqs~~~~~~~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpqqsqppppppppppqpppqs~~ssqjjjjjJJJJjjjjqsssssssqqjqs~~~~~~~~~~~~~~~~~~~~~~qpppppppppppppppp^^^^^^pp^^^^^^^!^^!^^^!!^^^^^^^s^^^^^^^^^^^^!!^!!!!!^!!^^^^^^^^^^^^^jjjrrjjjjjJJJJJJJJJJrrrrJJJJrrJJJrrJJJJJJJJJJJJJJJJJJJJJJJjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~s^^!!!^^^iiiivrvii^^^!^^^^ppppppwwwwwwwpwpppppppppwpppwpwwppwppppddddddddddrrppppddddpppppppgggqs~~sqqqqss~~~sqjjjJjjjjjjjaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqssss~~~ssss~~~~sqjjjjjqqqssqsssqqqqsss~~~~~~~~sqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qppppqppppppppppppppppqs~~~sqqqjjjJJjjqqqs~~ssssqjjjjqs~~~~~~~~~~~~~~~~~~~~sqppppppppppppppp^^^^^^p^^^^!!^!!!!!!!!!!^!!^^^^^^^^^^^^^^^^!!!!!!!!!!!!!^^^^^^^^!!^^^^jjjjrjjjJJJJJJJJJJrJJJJJJhJJJrrrJJJJJJJJJJJJJJJJJJJJJJJJJJjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~ss^^!!!^^^iivvvrviii^^^!^^^^pwppwpwwwwwwwwwwwwpwppppppwwwpwwwpppppdpddddddddprrpppddddpppppppqqqs~~~qjjjjqqs~~~sqjjjjjaaaaaaaq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssssssssqqqqssssssqqjqqssssqjqqsssssss~~~~~~~~sqjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qpppppppppppppppppppppqs~~~~~sssqqjjjjqsss~~~~~~sqjjjjqs~~~~~~~~~~~~~~~~~~~ssqppppppppppppppp^^^ppp^^^^!!!!!^^^!^^^!!!!!!!!^^^^!!!^^!^!!^^^^^^^^^!!!^^!^^!^!!!^^^^^jjjjjrrjJJJJJJJJJrJJJJJJJhhJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~s^^^!!^^^^ivvvvrviiii^!!!^^^pwwpwwwwwwwwwwwwwpwwppwwppwwwwwwppppwppppppddddppprrpppddpppppppqsss~~~sqjJjjjjqs~~sqjjjjaaaaaaaaq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~sssqqqqjjjjqqqqqsssqsssqqqjjjjqqqsss~~~~~~~~sqjjjqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppppppppppppp^^^pppppqs~~~~~~sssqjjqss~~~~~~~sqjjjjqs~~~~~~~~~~~~~~~~~~~~~ssqpppppppppppppppppp^^^^^^!!!!^^^!^^^^^^^!!!!!^^^!!!!!!!!^^^^^^^^^^^^^^^^!!!!!!!^^^^^jjjjjjjjrJJJJJJJJrJJJJJJJhJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJjjjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~ss^^^!!^^^^ivvvvrvviii^^!!^^^wwwwwwwwwwwwwwwwwwwwwpwwpwwwwwwwwpwpppppppppddppppprpppddppppppqs~~~~~~sqjjJJjjqs~~~sqajjaaaaaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjjjjjjjjjjjqqsssqqjjjjJjjjjjqqs~~~~~~ssqjjjJjqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~sqppppppppppp^p^^^^pppppqss~~~~~sssssqqss~~~~~~~~~sqqjqs~~~~~~~~~~~~~~~~~~~~~sqqpppppppppppp^^^^^^^^^^!!!^!^!^!!^^^^^^^^^^!!!^^!!!!!!!!^^^^^^^^^^^^^^^^^^^^^!!^^^^wjjjjjjjjjjrrJJJJJJrJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJyJJJJJJJJjjjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~sss^^!!^^^iivvvrrvviii^^!!!!^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwppppwppppppppppprpppdppppppqs~~~~~~~sqqjJjjq~~~~~qaaaaaqqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjj^^jjjjjjjjjjjqqqjjjjjjjjjjjjjjqs~~~sqqqjjjJJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqqqs~~~ssqpppppppppp^^^^^^^^pppppqsss~~~~~~~ssss~~~~~~~~~~~~ssqs~~~~~~~~~~~~~~~~~~~~ssqppppppppppp^^^^^^^^^^^^^!!!!!^^!^^^wwwww^^^^^!!!!!^^^^^^^^^^wwwwwwww^^^^^^^^^^^^^^^wwwjjjjjjjjjjjrrrrrrJJJJJJJJJJJJJJJJJJJJJJJJJJJJyJJJyyJJJJJJJJJjjjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~ss^^!!^^^iivvvrvvvii^^^^!^!^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwppwwwpwppppppppprppppppppppq~~~~~~~~~sqjjjq~~~~~~sqaaaaqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqjj^^^jjJJjjjjjjjjjjjjjjjjJJJJJJjjjqs~sqjjjJJJJjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqdddqsssqsqpppppppp^^^^^!^^ppppppqss~~~~~~~~~~ss~~~~~~~ss~~~~~~~~~~~~~~~~~~~~~~~~~~sqsqqppppppppp^^^^^^^^^^^!!^!!!!!!!^^^^wwwwwww^^^^!!!^^^^^^^^^wwwwwwwwwwwwwwwwww^^^^^^wwwwjjjjjjjjjjjjJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJyyyJyyJJJJJJjJjjjjjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~ss^^^!^^^iivvvvrvvvvii^^^!!!^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwpppppwpppppppppprpppppppppq~~~~~~~~~~~sqqq~~~~~~~~sqaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssssqjj^^^jjjjJJJJjjjjjjjjjjjjJJJJJJjjjjqs~sqjjJJJJJJJJjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddqqqdqsqppppppp^^^!^^^pppppppqss~s~~~~~~sss~~~~~sssssss~~~~~~~~~~~~~~~~~~~~~~ssqpqppppppppppp^^^^^^^^^!^^^^!!!!!!^^^wwwwwwwwww^^^^^!^^^^^^^^wwwwwwwwwwwwwwwwwww^^^^^wwwwjwwjjjjjjjjjjJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJyyyJJyJJJJJJJJJJjjjjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~ssss^^^^!!^^iivvvvrvvvvii^^^!!!^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwppwwppppppppppppprrppppppppqs~~~~~~~~~~~ss~~~~~~~~~~qaaq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqsssqjj^^jjjJJJJjJJjJJjjJJJJjJJJJJjjjjjq~~~sqjJjjJJJJjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqqddddddddddddqpdpppp^^^!!!^^ppppppppqsss~~~sssssssss~ssssssqqqsss~s~~~~~~~~~~~~~~~~ssqpppppppppppppp^^^^!^!!^^!!^^!!^!^^^^wwwwwwwwwwwww^^!!^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjjjwjjjjjjjJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJyJJJJJJJJjJjJjjjjjjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~ss^ss^^^^^!^iiivvvvrvvvviii^^!^!^^^^w^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwpppppppppppppprppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~qq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxqssqjj^jjjJJJJjJJJJjJJjJJJJJJJJJJjjjjqs~~~~sqjjjjJJjjqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqqqddddddddddddddddpddpp^^!!!^^ppppppppppqss~ssssssqqqqsssssqqqpppqqss~~sss~~s~~s~~~~~~sqppppppppppppppp^^!!!!!!!!!!!!!!^^^^^wwwwwwwwwwwwww^^!^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjwwwjjwjjjjjjJJJjJJjjJJJJjJJJJJJJJJJJJJJJJJJyyJJJJJJJJjjJJJjjjjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~s^^^^^^^^^!^iiivvvvrvvviiii^^^^!^^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwppppppppppppprpppppppqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxqqqjjjjjjjJJJJJJJJJJJJjJJJJJJJJjjjjjqs~~~~~sqqqjjJjqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqdddddddddddddddddddd^^pp^^!!!^^^^ppppppppqsss~ssqqqppppqqqqqppppppppqssssssssssssss~~~sssqqpppppppppp^^^^!!!!!!!!^!!!^^^^^^^^wwwwwwwwwwwwww^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjwwwjjjjjjJjjJJjjJJJJjJJjJJJJJJJJJJJJJJJJyJJJJJJJJJJJJJJjjjjjjjqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~ss^^^^^^^^!^^iivvvvvrvvviiii^^^!!^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwpwpppwpppwpppprpppppppqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~~s~~sssqxxx^xxxxqjj^j^^jjjJJJJJJJjJJJJJJJJJjjjjjqqs~~~~~~~sssqjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddddddddddddddddd^^^^^^!!^!!^^^^^pppppppqqssqqppppppppppppp^pppppppqsqqqqqqqqqsssss~~~sssqpppppp^^^^^^^^^^^!!!!!^^^^^^^^^^wwwwwwwwwwwwww^^^^^^^www^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjjwjjjjjjjJJjjJJJjjJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJjjjjjjqqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~ss^^^^^!!!^^iiivvvvvrvvvviii^^^!^^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwppppppppppprppppppqqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sbbs~~~~~~~ssssqqqqxxxx^^xxxxj^^^^jjjjjjJJJJJJJJJJJJJjjjjjqqss~~~~~~~~~~~sqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddd^dd^^d^^dddddddd^^!^^^!!!!!!!^^^^^ppppppppqqpppppppppppppp^^^^ppppppqpppppppppqssss~~sssqppppppp^^^^!^^^!!!!^!!^^^^^wwwwwwwwwwwwwwwwwwwwwww^^^^w^^!^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjjjjjjjjjjJJJJjjJJJJJJJJJJJJJJJJJJJJJJjjJJJJJJJJjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~ss^^^^^^!!^^^iiivvvvvvrvvviii^^!!^^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwpwpppppppppprrppprrsssqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sbwwbs~~~~~sqqqqxxxxxxx^^^xxxx^^^^aajjjjjjjjJJJJJJjjJjjqjjqss~~~~~~~~~~~~~~sss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddd^^d^^^^^^^^^d^^dd^^!!!!!^!!!!!!^!^^ppppppppppppppppppppp^^^^^^^^^^pppppppppppqqsss~ssssqqqpppppp^^^!!!!!!^!^!^!^^^^wwww^^wwwwwwwwwwwwwwwwwwwwww^w^!^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjjjjjjjjjjjjjJjjJJJJJJJJJJJJJJJJJJjJjjJJJJjjjjjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~s^^^^^^!!^^^iiiivvvvvvrvvviii^^!!^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwppppwpppprrrrrqqqqppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sbwwbsssssssqxxxxxxxxxx^^^^^^^xxx^^aajjjajjjjjjJJJJJJjjjqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddd^^^^^^!^^!!^^^^^^dd^^!!!!!^^!!!!!!!^pppppppppppppppppp^^^^^^!!!!^^^^ppppppppqqsssssssssqpppppppp^^^^^^!!!!!!!!!!^^^^ww^^^^^wwwwwwwwwwwwwwwwwwwwww^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjjjjjjjjjJJjJJjjjJjJJJJJJJJJJJJJJyyJJjjjjjjjjjjjjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~s^^^^!!^!^^^iiiiivvvvvrrvvvii^^!!!^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwpwppppppppppppppppppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sbwwwwbssssbxxxxxxxxxxx^^^V^^^^^^xxaaaaaajjjajjJJJJJJJjjqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddd^^^!^^!!!!^^!!!!!^^^d^^^!^^^^^^!!!!!^^^pppppppp^ppppppppp^^^!!!!!^^^^ppppppppqsssssssqqqqqpppppppp^^^^^^!!^^^^!!!!^^^ww^^!!^wwwwwwwwwwwwwwwwwwwwwwww^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjwjjjjjjjjjjjJJJJjjjjjjjJJJJJJJJJJJJJJyJJJjjjjjjjjjjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~s^^^^^!!!^^^^iiiiivvvvvrvvii^^^^!^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwpppppppppppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssbbbbbbs~~~ssss~~~~~~~~~~~~~~~~~~~~~~~~~~~s~bwwwwbsssbbwxxxxxxxxxx^^^LLLV^^^^xxaaaaaaaaajjjJJJJJjJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddddd^^d^^!^^^^^^!!^^^ddd^^^^^^^^^!!!!!^^^pppp^^^^^^ppppppp^^^!!!^^^^^pppppppppppqqqqqqqppppppppppp^^^^^!^^^^^^^^^^^!^^^ww^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjjjjjjjjjjjjJJJjjjjjjJjJJJJJJJJJJJJJJJJjjjjjjjjjjjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~ss^^^^!!!^^^^iiiii^^vvvrvii^^^^^!^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwppppppppppppppwwwbbss~~~~~~~~~~~~~~~~~~~~~~~~~~~~sbbbwwwbssssssbbbs~~~~~~~~~~~~~~~~~~~~~~~~~~~bwwwwbsssbwwwwxxxxxxxxxx^^LLL^^^^xxxaaaaaaaaajjJJJJjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qddddddddddd^^^^^d^^^^^^^ddd^^^^d^d^^!^!!!!!^^^^pp^^^^!^^pppp^^^^!!^^^^ppppppppppppppppppppppppppppppp^^^^^!!^^^^^^^^^^^^^^ww^!^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjwwjjjjjjjjjjjjJjjjjjjJJJJJJJJJJJJJJJJJJJjjjjjjjjjjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~ss^^^!^!^^^^^iii^^^vvvrvv^^^^^^!!^^^^wwwwwwwwwOwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwppppppppwpwwwwwwwbbsss~~~~~~~~~~~~~~~~~~~~~~~~~sbwwwwbssssbbbwwbs~~~~~~~~~~~~~~~~~~~~~~~~~~ssbbbbssssbwwwwxxxxxxxxxxx^^^L^^^xxxxaaaaaaaajajjjJJJjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqdddddddddd^^ddd^^^dddddddddddd^!!!!!!^!!^^^^^^^^!!!^ppppp^^!!^^^^^^ppppp^^ppppppppppppppppppppp^^^^!!!!^^^^wwwww^^^^^^w^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjjjjjjjjjjjjjjjJjJjjJJJJJJJJJJJJJJJJJjjjjjjjjjjjjjjjqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~ss^^^!^!^^^^^ii^^^^vvvrvv^^^^^!!!^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwpppppppwwwwwwwwwwwwbbbsssss~~~~~~~~~~~~~~~~~~~~sbwwwwwbssbwwwwwwbs~~~~~~~~~~~~~~~~~~~~~~~~~~ssssss~~sbwwwwwwwxxxxxxx^^^^^^xxxxxxaaaaaaajjjjjjJJjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssqddd^^ddddddddddddddddddddddd^^!!^!!^!!!!^^^^^!!!!!^^pppp^^^^^^^ppppppp^^^^ppppppppppppppppppppp^^^!!!^^^^^wwwwwwwwwwwww^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjjjjjjjjjjjjjjjJJJjjJJJJJJjjJJJJJJJjjjjjjjjjjjjjjjjjqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~s^^^^!!!!^^^^^^^^^^vvrvv^^^!!!!!^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwpppppwwwwwwwwwwwwwwwwbbbbss~~~~~~~~~~~~~~~~~~sbwwwwwwbsbwwwwwwwbs~~~~~~~~~~~~~~~~~~~~~~~~~~~ssss~~~ssbwwwwwxwwxxxxxxx^^^xxxxxxxxxaaaaajjjjjjjjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~sssqddd^^^^dddDDddDDddddddddd^^^!^^^^^^!!!!^!!!!!^!!!^^^^^pp^^^ppppppppp^^^^^^ppp^^ppppppppp^^pppp^^^^!^^^^wwwwwwwwwwwwwww^wwwwwwwOwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjjjjjjjjjjjjjjjJJJjJJJJjJJJJJJJJJJJJjjjjjjjjjjjjjjqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~s^^^^!!!!!^^^^^!^^^^vrvv^^^!^!!!!^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwpppwpwwwwwwwwwwwwwwwwwwwbs~~~~~~~~~~~~~~~~~sbwwwwwwwbbwwwwwwwwbsssssss~~~~~~~~~~~~~~~~~~~~ssbbsss~sssbwwwwwwwwxxxxxxxxxxxxxxxxxxxxaaqqqqqjjjjjjjqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~~~~~~~~~~~~~~~~~sssssqdd^!!^dDDDDDDDddddddpddd^^^^^^^^^^^^!^!!!!!!!!^!!!^^^ppppppppppppp^^^!^^^^^^^^^^ppppppp^^pppp^^^^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjjjjjjjjjjjjjjjjjjJjjJJjjjjJJJJJJJJJJJjjjjjjjjqqqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~s^^^^^!^!!^^^!!!^^^^rrv^^^^!!!!^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwpwwwpwwwwwwwwwwwwwwwwwwwwbs~s~~~~~~~~~~~~~~~bwwwwwwwwwwwwwwwwwwwbbbbbbbs~~~~~~~~~~~~~~~~~~~sbwwbs~~~ssbwwwwwwwwwxxxxxxxxwwxxxxxxxxxxqsssssqqjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqqss~~~~~~~~~~~~~~~~~~~~~s~sqqqssqdd^^dddDDDDDDDDDdpddddddddi^ii^^^^^^^^!^!!!!!!!!!^^^^ppppp^^^^pp^^^!!^^^^^^^^^^^^pppp^^^^^^pp^^pbbbwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjJJJJJjJJjjjjjjjjqsssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~ss^^!!!!!!!!!!!!!^^^^r^^^^^!^!!^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbsssbss~~~~~~~~~~~~sbwwwwwwwwwwwwwwwwwwwwwwwwwbs~~~~~~~~~~~~~~~~~ssbwwbsss~sssbwwwwwwwwwxxxxxxxwxwxxxxxxwxxqss~~~~ssqjjjqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqdddqqs~~~~~~~~~~~~~~~~~~~sssqdddqrrddddddDDDDDDDDddddpdddddddiiiiiii^^^^^!^^!!^^^!!^^^^pppp^^^^^^^^^^^!!^^^^^^!!^^^^^^p^^^^^^^^ppp^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwOwwwwwwwwwwwwwwwwjwwjwjjjjjjjjjjjjjjjjjjjjjJJJJJJJJjjjjjjjqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~s^^^!!!!!!!!!!!!!!^^r^^^^!!^!^^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbbbbbbs~~~~~~~~~~~sbwwwwwwwwwwwwwwwwwwwwwwwwwwbs~~~~~~~~~~~~~sssbbwwwbss~~ssbwwwwwwwwwwwwwxxxwwwwwwxxxwwwbs~~~~~~~~sqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddddddqs~~~~~~~~~~~~~~~~sssssxdxddddrrdddddddDDdddddpppdpddddppiiiiiii^^^^^^^^^^^^!^^^pppppp^^^!!!^^^!!!!!!!^^!!!!!^^^^^^^^!^^^^^^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjjjjjjjjjjjjjjjjjjjjjJJJJJjJjjjjjqqqsss~~~~~~~~sqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~s^^^^!!!!!!!!!!!^!^^^^^^!^!!!^^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbs~~~~~~~ssssbwwwwwwwwwwwwwwwwwwwwwwwwwwwwbs~~~~~~~~~~~sbbbwwwwwbbs~~ssbwwwwwwwwwwwwwwxwwwwwwwwwwwwwbs~~~~~~~~~~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqdddddddddqs~~~~~~~~~~~~~~~SSSSSxddxdddddrddddddddddddpdpdddddpppppppiiiiii^^^^^^^^^^^^^pppppp^^^^^!!!^^!^!!!!!!^!!!!^!!^^^^^!!^^^!!^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjjjjjjjjjjjjjjjjjjjjjjjJJJJJJJJjjjqsss~~~~~~ssssqjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~s^^^^!!!!!^^^!!!!!!^^^^!!!!!^^^^^w^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbbs~~~~~~~~bbbwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbs~~~~~~~~~~sbwwwwwwwwwwbs~ssbwwwwwwwwwwwwwwwwwwwwwwwwwwbbss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddddddqs~~~~~~~~~~~~~ssSSSSSxxxxdddddrdddddddddddddpppddppppppppppiiiiii^^^^^^iii^^pppppppii^^^^^^^!!!!^!^!!!!!!!!!!!^!^^!!^^^!!^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjjwwjjjjjjjjjjjjjjjjjjjJjjJJJjjjjqs~~~~~~ssqqqqjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~sss^^^!!!^^^^^^!!!!^^^^!^!!!^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwOwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbsss~~~~~~~sbwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbs~~~~~~~~~sbwwwwwwwwwwbs~sbwwwwwwwwwwwwwwwwwwwwwwwwwwbsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqddddddddddddqss~~~~~~~~~s~SSSSSSSSSSxdxdddddrrrrrrrrrddddpppppppppppppppiiiiiii^^^iiiiiippppppppiiii^ii^^^^^!^!^!!^^!!^^!!!!!!!^!!!!^!!^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjwwwwwjjwjjwwjjjjjjjjjjjjjJJjJjjjjqss~~~~~sqjjjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~ss^^^!^^^^^^^^!!!^^!!!!!!!^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbsss~~~~~~~sbwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbs~~~~~~~~~sbwwwwwwwwwbs~ssbwwwwwwwwwwwwwwwwwwwwwwwwwwbss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqsqdddddddddddddqqsss~~~~s~~ssSSSSSSSSSxxdddddddddddddddrrddpdpppppppppppppppppppiiippppiipppppppppiiiiiiiii*^^^^^^^!!^!!!!!!!!^!^!!!^!!!!^^^^^ww^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjjwwjjjjjjjjjjjjjJJJJjjjjqssss~sssqjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~s^^^!!^^^^^^^!^!!!!^!!^!!^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbbss~~~~~ssbwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbs~~~~~~~~~~sbwwwwwwwwbs~~sbwwwwwwwwwwwwwwwwwwwwwwwwwwbss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssqddqddddddddddddddddqqsssss~~ssSSSSSSSSSxxxxxxxdddddddddddddrdddpppppppppppppppppppppppppppppppppppppiiiiiiiiir^^^^^^^^^^!^^^^!!!!!!!!^!!!!!^^^^^^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjwwwwwjjjjjjjjjjjJJJjjjjqsssqqsqqqjjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~ss^^!!^^^ss^!!^^!!!!!^^^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbss~~~sbwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbbs~~~~~~~~~~sbwwwwwwbs~~ssbwwwwwwwwwwwwwwwwwwwwwwwwwwbss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqqqddddddddddDDdddddddddqqqqss~ssssSSSSSSSSSSSSxxxddddddddddddrddppppppppppppppppppppppppppppppppppppppppiiiiiiiri^^^^^^^^^^^^^^^^!!^!!!!^^!!!!!!!^^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjjww^^jjjjJJjjjjjjqssqjjqjjjjjjJJJJjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~ss^^^^^^ss^^^^!^!!!!^^^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbs~~~~ssbbwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbss~~~sss~~~~ssbbwwwbs~~~ssbwwwwwwwwwwwwwwwwwwwwwbbbbbss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddddddddddddDDddddddddddddqsssssssssssSSSSSSSSSxddDdddDDddddrdddpppdddpppppppppppppppppppppddppppppppppiiiiiirriiiiii^^^^^^^^^^^^^^^!!^^^^!!!!!!!!^^^^w^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwjwwww^^^^jjjjjjjjjqssqjjjjjjjjJJJJJjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~s^^^^^^ss^^^^!!!!!^^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbbss~~~ssbwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbbsssssbbbs~~~~~ssbwwbs~~~sssbwwwwwwwwwwwwwwwwwwwbssssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddddddDDdDdddDdddddddddddddqssssssssssSSSSSxSSSxddDDDDDDddddrddddpdddpppppppppppppddpdppppdddppppppppppppiiiriiiiiiiii^^^^^ii^^^^^^^^^^*^^^!^!^!^!^^^^^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^^^^^jjjjjjjjqsssqjjjjJJjjjJJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~ss^^^^ssssss^!!!!!^^^^^ww^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbs~~~~sbwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbssbbbbwwwbs~~~~~sbwbs~~~~~~ssbbwwwwwwwwwwwwwwwwwbssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddddddDdDDDDDDDdddddddddddddddxxsssssssrrSSSSSSSSxxddDDDDDDdDddrddddpdddpdpppppppddpddddpppddddddppppppppppppiriiiihhhiiiii^iiiiiii^^^^^^rr^^!!^^^^^^^!!!^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^!^^jjjjjjjjjqsssqjjjjJJJjJJJJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~s^^^sssss^^^^!^!^^^^^pp^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbss~~~sbwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbbwwwwwwwbs~~~~~~sbs~~~~~~~~~sbwbbbbwwwwwwwwwwwwbs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~sqdddddddddDDDDDDDDDDDdddddddddddddxSSSssssrRRrSSSSSxxxdddDDDDDDDDdddrddddpddddpppppdppdddddddddddddddpppppppppppppriiihhhhhiiiiiiiiiiiiiiiiiir^^^^^^^^^^^^^^!^!^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^^!^^jjjjjjjjjjqssqjjjjJJJjJJJJJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~ss^^^ssss^^^^!!!^!^^^ppp^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbs~~sbwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbs~~~~~~~s~~~~~~~~~~~sbssssbbwwwwwwwwwwbs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqsqqdddddddddDDDDDDDdDDDddddddddddddxxSSSSSSSSSRRrSSSxxdxdDDDDDDDDDDddddrrddddddddpppppddddddddddddddddddppppppppppprpiiiphhhiiiiiiiiiiiiiiiiiiir^^^^^^^wwww^^^^^^^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^!!!!^jjjjjjjjjjqsssqjjjjJJJJJJJJJjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~ss^^^sssss^^^!!!!^^ppppp^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbsssbwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbs~~~~~~~~~~~~~~~~~~~s~~~ssbwwwwwwwwbbss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddqdddddddddDDDDDDDDDDDDddddddddddddxxSSSSSSSSSSSrRrSSxxdddddDDDDDDdDddddddrdddddddpddpddddddddddddddddddpdpppppppppprppppphhpiiiiiiiiiiiiiiiiiir^^^^aaaawwwwww^^^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^^!!^!^^jjjjjjgqqsssqjjjjJJJJJJJJJJjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~sss^sssss^^^!^^!^^ppppp^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbssbwwwwwwwwwwwOwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbs~~~~~~~~~~~~~~~~~~~~~~~~sbwwwwwbbsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddddddDDDDDDDDDDDDDDdddddddddddxxxxSxSSSSSSSSSRRrSSxxddDDDDDDDDDDddddddrdddddpddddddddddddddddddddDddddddpppppppprpppppppppiiiiiiiiiiiiiiiiirp^^aaawwwwwwwww^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^!^^^^^^!^jjjjjjgqsssqjjjjjjjjJJJjJJJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~ssssss^^^!!!^!!^^ypp^^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbssssbwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbs~~~~~~~~~~~~~~~~~~~~~~~sbwwwwwbsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddDDDddDDDDDDDDDDDDDDdddddddddddddxdxxSSSSSSSSSSSSSrrxddddDDDdDDDDDddddddrdddDddddddddpddDdddDdddDdDDddddddpppppppprppppppppppiiippiiiiiiiirrrp^^aaaaawwwwaawww^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^!!^jjjj^^jjjjjjggqs~ssqqjjjjjjjJJJJJJJjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~ss^^!^^^^^^^^yy^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwOwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbssssbwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbs~~~~~~~~~~~~~~~~~~~~~sbwwwwwwbss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddDDDDDDDDDDDDDDDDDDdddddddddddddddddxxSSxSSSSSSSSRRRrdddddDDDDDDddddhddrdddDDdddddddpddDdddDDDdDDdDDddddddppddpppprpppppppppiipppprrrrrrrpppppaaaaaawwaawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^!^^jjjjjjjjjjjjjqs~~~sssqjjjjjjjjjJJJJjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~ss^^^^^^^^^^yy^^!!^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbssssbwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbbs~~~~~~~~~~~~~~~~~~~~~~sbbbwwwbs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddddddDdDDDDdDDDDDDDdDddddddddddddddddxxddxxSSSSSSxxddrrRRrdddddDDDDdddhhdddrddDDdDddddddddDddDDDdDDDDDDDDdddddddddppprppppppppppppprrpppppppppppaaaaaaaaawaaawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^^wjjjjjjjjjjjgjqs~~~~sqjjjjgjjjjJJJjJjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~ss^^^ssqyyyy^^^!!^^www^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbsssbwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbsss~~~~~~~~~~~~~~~~~~~~~~~sssbwwbs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddDdDDdDDDDDDDDDDDddddDdddddddddddddddddxxSxSxxdxdddddrRrddddddDDddddddddrddDDdDDDdddddDDDDDDDDdDDDDDDDdddpddddpppprpppppppppppprppppppppppppaaaaaahaaaawaaaawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^wwwj^^jjjjjjjjjqs~~~sqjjjggggjjjjJJJJjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~s^^ssssqyy^^^!!^^wwww^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbssbwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbss~~~~~~~~~~~~~~~~~~~~~~~~~~sbwbss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqgddddddddddDDDDDDDDDDDDddddDDdddddddddddddddxdxxxxdddddddddddRrdddddddddhddhdrddDDddDDDddddDDDDDDDDDDDDDDddddddddddddppddrxxxpppppppprpppppppppppppaaahhhhaaaawwaaaawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^www^^^^jjjjjjjjjqs~~~~sqjjqqqqqqjjJJJJjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~ssssssqyyy^^^!!^^^ww^^!^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbsssbwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbs~~~~~~~~~~~~~~~~~~~~~~~~~~~sbs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgdddddddddddDdDDDdDDDDDDDdddDDdddddddddddddddddxddxddddddddddrRrddddddddhhhhrdddDDDDDDDddDDDDDDDDDDddDDdddddddddDDdddddddxrSxxxpppprrpppppppppppppaaahhhhaawaaawawawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^www^^^^^jjjjjjjjjjqs~~~~sqqssssqjjjjJjjjjqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~ss^^yyyyy^^^!^^^ww^^!!^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbbs~ssbwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbs~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqggggdgdddddddddddddDDDDdDdddDddddddddddddddddddddddddddddddddrRRrddddddddhhhrdddDDDDDDDddDDDDdDDDDddDDdddddqdddddDddddddxSrSSxSxxrrpppppppppppppppaahhhhhaaaawaaawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^www^^^^^jjjjjjjjjjjjjqss~~~~ss~~~sqjjjjjjjjq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~sss^^^^yyyy^^!!^^^^ww^^!^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbss~~sbwwwwwwwwbwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqgggggdddddddddddddddDdDDDDdddddddddddddddddddddddddddddddddddrdrRRRrddddddrrrdddDDDDDDDDDDDDDdDDDDddddddddqlqqdddDDDdDDxSSrSSSSrrddpppppppppppppppppphhhaaaaaaaaawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^w^^^^^^^jjjjjjjjjjjajjqs~~~~sqqqssqjjjjjjqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~s^^^^^^^yyy^^!!!!^^ww^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbs~~~~sbbbbwbbbsbwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqgggggdddddddddddddddddDDDDDDdDDDddddddddddddddddddddddddddddddrddrrRRRRRRRRRRRrddDdDDDDDDDDDDDDDDDDdddddddqllllqdddDDDDDDxSrrrrrddddddpppppppppppppaaphhpahhaaaawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^^^^!^^^jjjjjjjjaajaaaqs~~sqaaaqssqjjjqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~s~~~ss^^^^^^^^yy^^^^!!^^wwww^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbs~~~~~~ssssbbsssbwwwwwwwwwwwwwwwwwwwwwwwwwwwwaawwwwbss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~sqqggggddddddddddddddddddDDDDDDDDDDddddddddddddddddddddddddddddddrddddddddddddddRrdddddDDDDDDDDDDDDDDDddddqqqlllllqdddddDDdddrrddddddddddppppppppppppppaaphahhhaaaaawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^^!!!!!^^jjjjjjjjjaaaaaqsssqaaaaqsssqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~s^ssss^^^^!^^^^yyy^^!!!^^wwwwwwwwwwwOwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbs~~~~sssssssssssbwwwwwwwwwwwwwwwwwwwwwwwwwwwaaawwabqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqss~ssssqgggggdddddddddddddddddddDDDDDDDDddddDDdddddddddddDDdddddddddddrddddddddddddddddRrrddddDDDDDDDDDDDDdDdddqllllllllqdqqdddddddrddddddddpdpppppppppppppppapppaahhhhaaawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^^^^!^!!^^^^jjajjajaaaaaaaqqqaaaaaaqs~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~s^^^ss^^^^^!^^^^^y^^^^!^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbs~sssbssss~~~ssbwwwwwwwwwwwwwwwwwwwwwwwwwaaaaaaaaaaaqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqgggqssssrqggggggdgdddgggddgdddddDdDDDDDDDDDDDDDDDdddddDdDDDDDdDDdddddddddrdddddddddddddddddRRrdddDDdDDDdDddDdddddddqllllllllqllqqdddrrddddddddddppppppppppppppaapppaaahhhhhaaaawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^^^^^!!^^!^^^^aaaajjjjaaaaaaaaaaaaaaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~ss^^^^^^^^^!!^^^^yp^^^^!!^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbssbbwbbbss~~~sbwwwwwwwwwwwwwwwwwwwwwwwaaaaaaaaaaaaaaqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqgggggqqqqrrgggggddgggggggggdddddDDdDDDDDDdDDDDdddDdddDDDDDDDDDDddddDdddddddrddDddDdddDddDddddrRdddddddDDdDddddddddddqllllllllllllqdqrddddDDDDdddppppppppppppppappppppphhhhhaaaaaaawwwwawaaaawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^w^^^^^!!!!^^^^^^aaaajjjaaaaaaaaaaaaaaaaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqs~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~ss^^^^^^^^!!!!!^^^^^p^^^^!!^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwbbsssbwwwwwbss~~ssbwwwwwwwwwwwwwwwwwwwaaaaaaaaaaaaaaaaaaaaqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~ss~~~~s~sssqppppppggggggrgggggggggggggggdddddddDDDDDDDDDDdDdDDDdddDDDDDDDDDDddddddDDdDdddrddDddDDdDdDdDDddddrRrddddddDdddddddddddddqllllllllllllqlrdddDDDDdddddddpppppppppppppppppphhhpppaahaaaawwwwaawwaaaawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwOwwwwww^^^^^^^^!!!^^^^^^aaaaaaaaaaaaaaaaaa^^aaaaqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qjjqs~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~s^^^^^^^!!!!!^!^^^^^pp^^^^!^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^wwwwwwbwwwwwwwwwwwbssssssbwwwwbbss~~ssbwwwwwwwwwwwwwwwwwaaaaaaaaaaaaaaaaaaaaaqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qsssqqs~~ssqqqqppppppggggggggrggggggggggddddggddddddddDDDDDDddDDddDDdddddDDDdDDDdddDdDDDDDdddrdDDDdDDDDddDDDDddddrRRdddddDddddddrrdddqqlllllllllllllllqdddddDDdddpdppppdddppppppppppppppppppaahhhhwaaawwwwaawwawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^^!!^!^^^^^aaaaaaaaaaaaaaaaaaaa^^^^aaqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjq~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~s^^^^^!^!!!!!!!^^^^^^ppp^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^awawbsbbwwwwwwwwbssssssbwwwwwwwbs~sssbwwwwwwwwwwwwwwwwaaaaaaaaaaaaaaaaaaaaaaapqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgqqqggqssqqppppppppppgggggggggrgggggggddddddggdddddddDDDDDDDdddddddddddddddddDdDdDDDDDDDDDddrdddDDDDDDDdDDDDDddddddrRddddddddddrddrrrlllllllllllllllllqddddddDDdddddpdddpdpppppppppppppppppphahhhaaaawwwwwaaaaawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^!!!^^^^aaaaaaaaaaaaaaaaaaaaa^^!^aaqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjJjqs~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~s^^^!!!!^!!!!!!!^^^^^^ppp^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^aaawbssssbwwwwwwbbsssssbbwwwwwwwbssssbwwwwwwwwwwawwwwwaaaaaaaaaaaaaaaaaaaapppppqqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qggggggggqqpppppppppppgggggggggggrgggggddddddgddddddDDDDDDDDddddddddddddddDDDddddddDDDDDDDDDDdrddDdDDDDDDDDDDDDDddddddrRRrdddddrrddddddqqllllllllllllllllqdqqdddDDddddppdddddpppppppppppppphpphpahhaaaawawwwwaaaaaawwwaaawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^^!!!^^^aa^aaaaaaaaaaaaaaa^aa^^!!^^apqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjJJjqs~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~s^^^^!!!!^!!!!!!!!^^^^^pppwwww^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^!^aaqsssssssbwwwwbsss~~sbwwwwwwwwwbsssbwwwwwwwwwwaaaawawaaaaaaaaaaapppaaaaapppppppppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqggggggggggpppppppppgggggggggggggrgggggddddddddddddDDDDDDDDDDddDdddddddddddDDDddDdDDDDDDDDDDDrDDDDDDDDDDDDDDDDDDDddddddrRRrdddrddddddddddqllllllllllllllqddqlqdddDDdddddddddddpppppppppppppppphhpppaaawwaaaaaawawaawwaawawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^^!!^^^^^^^^^aaaaaaaaaaa^^^^^^^!!^^ppqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjJJJjjqs~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~s^^^^!!!!!!!!^!!^!^^^^ppwwww^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^^aaaqssssssbbwwwbss~~~sbwwwwwwwwwbsssbwwwwwwwwwaaaaaaaaaaapappaappppppapaapppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggggggppppppppppgggggggggggrggggddddddddddDdddDDDDDDDDDdDDDdDdddDDDDdDDDdDDDDDDDDDDDDDDrDDDDDDDDDDDDDDdDDDDDdddddddrlqdrddddddddddddqqlllllllllllllqqllqddddDDddddDDdddpppppppppppppppphhhhhhaaaaaawaawwaawawwaaaaaawawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^^!^!!!^^^!^^^^^aaaaaaaaaa^^^!!^!^^^^^pppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjJJjjjqq~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~s^^^!!^^!!!!^!!!!!^^^^^^^www^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^^aaaqsssssssssbwbss~~~~sbbwwwwwwwwbssqawwwwwawaaaaaaaaaaaaaapppppppppppppappppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqggggggggggggpppppggppgggggggggggrgggggggddddddDDdddddDDDDDDDDDDDDDddddDDDDDDDDDDDDDDDDDDDDDrDDDDDDDDDDDdDDDDdDDDDDDdddddqllrrdddDDdddddDdddqlllllqlllllllllllqdddDDddDDDdddpdpppppppppdpppphhhhhhhhhaaaaaaaaaaaaaaawawawaawwwawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^^^!!!!^^^!^!!^^aaaaaaaaaa^^!!!^^^^p^^ppppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjJJJJjjaaqs~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~s^^!!^^^^^^!^^^!!!!!^^^^^^wwwww^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^^^aaaaqsssssssssbbbs~~~~~ssbwwwwwwwbssqaawwwwwwaaaaaaaaaaaaaapppppppppppppppppppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qggggggggggggggppppggggppggggggggggrggggggggdddddDDDddDdDDDDDDDDDDDDDDDDdDDDDDDDDDDDDDDDDDDDDDrDDDDDDdDDDdddddDdDdDDDDDddddqllqdddDdDDddddDdddqllllqdqllllllllllqddDDDDDDDDddpddpppppppdpddppphhhhhhhhaapaaaaaahaahaawwawwwaaawaawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^^^^!!!^^^^!!!!^aaaaa^^aaaa^^^!^^^^ppppppqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjJJjjjjaaaaqs~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~s^^^^^^^^^^^^^^!!!!!!^!^^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^!!^aaaqssssssss~sssss~~~~~~sbbwwwwwwbssqaaawwwwaaaaaaaaaaaaaappppppppppp^^ppppddppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qggggggggggggppppppgggggpppggggggggrggggggggggddDdDDdDDDDDDDDDDDdDDDDDDDDDDDDDDDDDDdDDDDDDDDDDDrrDDDDDDDDDdddddddDDDDdDddddqlllqddDDDddDddDdddqllqqqddqlllllqlllqddDDDDDDDddddpppppppddddddppphhhphpahaaaaaaaaaaaahhaaawwwawaaawawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^^^^!^!!!!!!!^^^^^^^^^^^aa^^!^!^^pppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjJjjajaaaaaqss~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~s^^^^^^yyy^^^^^^!!!!!!!!^^^^^^^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^!!^^aaaaqqqssss~~s~~ss~~~~sssssbwwwwwbsqaaaaawwaaaaaaapaaapppppppppppppp^^^ppddddpdppqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggggggpgggppgggggggpggggggggrgggggggggddddddddddDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDrrDDDDDDDDddDdDdddddDDddddqlllDddDDDDDDdDDdddqlqddddqlllllqdqlqdDDDDDDDDDdddddpppdpddddddddppphhpppaappaaaaaaaaahhhhaaaaaawwwawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^^^^!!!!!!!!!^^^^^^^^^!!^^^^!!!!^^^ppppqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqjjjaaaaaaaapqqqs~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~s^^^^yyyyyyydd^^^^^^^^^^!!!^!^^^^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^!^^aaaaaaaqssss~~~~~~~~~~sbbssbwwwwbbssqaaaaaaaaaaaapppappppppppppppppp^^pppdddddpppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqgggggggggggggggpggggggggggggggggrgggggggdddddddddddDDddDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDdrDDDrrrrrrrddddddddddddqlllqdddDdDDDDDDDDdddqdddqqlllllqddqlqdddDDDDDDdddpdppppdddddDDdddppphhppppapppaaaaaaaahhhhhaaaaaaaawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^^!^!!!!!!!!!^^^^!!^^^!!!^^^^!!!^^^ppppqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqaaaaaaaappppqs~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~s^^^^yyyyyyddd^^^^^^^^^^^!^!!!^!^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^^^aaaaaaaaqss~s~s~~~~~~~sbwbssbwwwbsssqaaaaaaaaaappappppppppppppppp^^pppppddddddpppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqgggggggggggggggppgggggggggggggggrgggggddddddddddddddddDdDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDrrrDDDDDDdrrdddddddddqlllqddddddDDDDDDDDdddddddqlllllqdddqllqddDDDDDDddppppddpdddDDDdddpdppphppppppppppaaaaaaaphhhahhaaaawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^w^^^^!!!!!!!!!!!!^!!!!^^^!^!!!^^!!^^^dddpppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqaaappaaappppq~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~s^^yyyyyyyddddd^^^dd^^^^!!!!!!^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwaawwwwwwwwwwwwwwwwwww^^!^aaaaaaaaaaqqs~~~~~~~~~~sbwwbssbbbbssqppaaaaaaaaaapppppppppppppppp^^^pppddddddppppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqggggggggggggggggggggggggggggggggrggggggdddddddddddDDddDDdDDDDDDDDDDDDDDdDDDDDDDDDDDDDDDDDDDDDDDDrDDDDDDDDDddrdddddqqqlllqddddddddDDDDDDDDdddddddqqllllqdddqllqddDDDDDdddppdddppddddDdddpppppppppppppppppppaaaaaahhphaawawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^^^^!^!!!!!!!!!!!!!!!^^^^^^^^^^^^^^^^dddpdqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpappppapppppq~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~s^qqyyyyqdddddddddddd^^^!^!^!!^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwaaawwwwwwwwwwwwwwwwwww^!^^aaaapaaaaaapqqs~~~~~~~~~sbbsssssssssqpppaappaaaapppppppppppppppp^^^^dppddddddppqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggggggggggggggggggggggggggrgggggggdddddddgdDDDdddDDDDDDDDDDDDDDddDDDDDDDDDddDDDDDddDDDDDDDDrDDDDDddddddrrdqqllllllqddddddDDDDDDDDDdDddddddddqllllqddqllqddDDDDDDddddddddpppdddddppdppppppppppppppppppaaaaaapaaaaawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww^^^wwwwwwww^^^^w^ww^^^^^^^^!!!^!!^!!^^^!^!^^^^*r^^^^ddddddddpdddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qpppppppppppqs~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~s^sqyyyqsqqdddddddddd^^!!^^^!^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwwaaawwwwwwwwwwwwwwwwwww^^^^^aaaaapppaaapppqs~~~~~~~~~sbs~~s~ss~sqppppppppaaapppppdddppppppp^^^^ddpppddddpppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggggggggggggggggggggggggrgggggggggddddddddDDDDdddDDDDDDDDDDDDDdDDDDDDDDDddDDDDDDdDDDDDDDDDDrDDDDDDdDddddrlllllllllqqddddddDDDDDDDDdDdDdddddqlllllqqlllqdddDDDDDDDddddddpppppdddppppppppppppppppppppppphhpaapaawawwwawwwwwwwwawwwwwwwwwwwwwwwwwwww^^^^^^wwwww^^^^^^^^^^^^^^!!!^!!^^!^^^^^^^^^^^^^^^rdddddddddppddddddqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqpppppppppqs~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~ssqyyqs~sqddddddddd^^^!^^p^^^^^^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwaaaawwwwwwwwwwwwwwwww^^!!!^^aaappppppppppqs~~~~~~~~~~s~~~~~~~~ssqpppppppppppppppddpppppppd^^dddddppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqggggggggggggggggggggggggggggrggggggggdddddgddddddddddddDDDDDDDDDDddDDDDDDDDDddddddDddddDDdDDDDDDrDDdDDDDDddddqllllllllllqddddDDDDDDDDDDDDDddddqllllllllllqddqdddDDDDDDDdddpdpddppdpppppppppppppppppppppppphhhpapaaaaawaawwwwwawwwwwwwwwwwwwwwwwwwwwww^^^^^^^www^^^^^^^^^^^^^!!!!^!!^!!^^^^^^^^^^^^^^dddrdddddddpdddddddqssss~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqppppppppq~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~ssqyqs~~sqqqyyddy^^!!^^^pp^!!^wwwwwwwwwwwwwwwwwwwwwwwwwwwwwawaaaawpwwwwwwwwwwwwww^^^!^^^aappppppppppqs~~~~~~~~~~~~~~~~~~~~~sqpppppppppppddpdddppdpp^pddddddqqqqqppqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqggggggggggggggggggggggggggggrgggggggddddddggdddddddDDdddDDDDDdDDdDDDDDDDDDddddddDddddddDddDDDDDDrDDDDDddddddddqllllllllqdddddDDDDDDDDDDDDDdddqlllllllllqllqqlqdddDDDDDddddddddddppppppddppppppppppppppppppphhhpahhaaaaawaawwwawwwwawwwwwwwwwwwwwwwwww^^^^!^^^ww^^^!!!^^!^^^^^^^!^^^^!!^^^ii^^^^^^dddddddrdddddddddddddqssqqqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppppppq~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~sqs~~~ssssqqyyy^^^^^pppp^^!^^wwwwwwwwwwwwwwwwwwwwwwwwwwwwaaaaaaawwwwwwwwwwwwwwww^^^!!^^aapppddppppqs~~~~~~~~~~~~~~sss~~~~sqdpppppppppddppdpddddd^^dppddddqsssqpq~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssqgggggggggggggggggggggggggggrggggggddddddgggddgggdddDddDDDDDDDdDDdDDDDdddDddddddddddddddddddDDdDrDDDDDddDddddddqlllllqqdddddDDDdDDDDDDDDDDdddqllllllllqdqllllqddddDDDDDDdddddddddppppddppppppppppppppppppppphpaahhhaawaaawawwwwwaawwwwwwwwwwwwwww^ww^^^^^!!^^^^^^!!^!!!!!^^^^^^^^^^^^^^^iiiiiiddddddddddrdddddddddddddqsqdddddqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppppppq~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~ss~~~~~sssqyy^^p^^^pppp^^^^^www^w^^wwwwwwwwwwwwwwwwwwwwwaaaaaawaawwwwwwwwwwwwwwww^^!^^ppppdddpppdqss~~~~~~~~~~~~sqqqs~~~sqddpdddpdppdddpdddd^^^^ddddddddqs~ssq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~ssrrggggggggggggggggggggggggggggrggggggggdddddggggggdddddddDDDDDDdDDDDDDDddddddddddddddddddddddddddrDDDDDdddddddddddqlllqddddddDDDdDDDDDDDDDDdddddqqqlllllqddqllqddddDDDDDDDDDdddddpdpppppdpdppdpppppppppppppppppppahhhaaaaaaaaaaawwwawwwwwwwwwwwwwww^^^^^^^!!!!^^^^!!!^!!!!!!^^*r^^^^^^^^iiiiiiiddddddddddddrddddddddddddrqdddddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qppppppqs~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqyyppp^^ppp^aaa^^waw^^^^wwwwwwwwwwwwwwwwwwwwaaaaaaaaaawwwwwwwwwwwwwwwww^^^^pppdddpdddddqs~~~~~~~~~~~sqdddqs~sqddddddddpppddddpdddd^^^^ddddddqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~sssRRrggggggggggggggggggggggggggrgggggggggggddggggggdddddddddDDDDdDDDdDDDdddddddddddddddddddddddrrrrDDDDDDDDDdddddddqlllqdddddDDDDDDDddDDdDDDDddddDdddqqllllqdqlqddddDDDDDDDDDDDdddddddpppppddddpppppppppppppppppppphhhhhaaaaawaaawwaaawwwwwwwwwwwww^^^^^^^^!!!^!!^^^!!!!!!!!!!^^ir^^^ii^^iiiiidddddDddddddddddrdddddddddrrdddddddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqqqs~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqyppppppppppaaaaaaa^^^^^wwwwwwwwwwwwwwwwwwwawaaaaaaaawaawwwwwwwwwwww^^ww^^ppppdddddddddqsss~~~~~~~~sqddDddqssqddpdddddpppppddddddd^^^^^dddqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqssssqrRRrggggggggggggggggggggggggrggggggggggggggggggddddddddddddDdDdDDddDddddddddppdqdqqqdddddddrrddddDDDDDDDDdddddddddqlllqddddddddddddDDDDDDDdddddDDddddqllqdddrddddDDDddDDDDDDDDDddddpdppdddddddppppppppppppppppppphhhhhhaaaaaaaaaawawwwwwwwwwwwwww^^^^^!!!!!!!!^!!!!^^^^!!^^^^iiriiiiiiiiidddddddDDddddddqddddrdddddddrdddddddDddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~sss~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppppppqqppaaaaa^^^^^wawwwwwwwwwaawwwwwwwaaaaaaaaawaaawwwwwwwwwww^^^^ppppppdpdddddddddqqsss~~~~~~sqdDDddqssqdddddddpdpppddddddd^^!^!^dqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqdddqqqqdddRRrrggggggggggggggggggggggrgggggggggggggggggddddddd^dddddDDDdddddddddddddpqqqlqlllqqqdddrdddddDDDDDDDDdddddqddqqlllllqqddddddpddddddDDDDDDddDDDDddddqrddddrdddDDDddDDDDdDDDDdddddddddddddddddppppppppppppppggpphhaahhahhaaaaaaaaawawwwwwwwwwwwww^^^!^!!^!!!!!!^!!!!^!^^^^^iiiiriiiiiiiddddddDDDDdddddqlqddddrddddddrdddddddDDDdddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqppppqsqpqqaaaaa^^^^aaawpwwwwaaaawwwpwaaaaaaaaaaaaaawwwwwwwwwwww^^^^^ppp^ddddddddddddddqss~~~~~~~sqddqqssqddddddddddddppdddDDd^^!!!^dqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqddddddddddddRRRrgggggggggggggggggggggrgggggggggggggggggd^dd^^dddddDddDdddddddddddddpqlllllllllllqrrdddddDDDDDDDddddqqdqqqlllllllllqddddpppdddddDDDDDDDDDDDDDddddrrrddrdDDDDddddDDDDDDDdddddddddpddddddddddpppppppppppppggghaggghaphhhaaaaawwwwwwwww^^^wwwww^^^!!!^!!^^^!!!!^^!!^^^^^^iiiddriiddddddddDDDdDdddddqllqqdddrdqqqdrddddDdDDDdDdddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqqqpqssqssqqaaa^aaaawaawwwwaawaaawwwaawaaaaaaaaaaaawawwwwwwwwww^^^^^^^^^ddddddddddddddqss~~~~~~~sqddqs~sqdddddddddddddpddDDDdd^^!^^dqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qddddddddddddDDdrRRgggggggggggggggggggggrggggggggggggggggg^^dd^^dddDDDDddddddddddddqqqqllllllllllllrrdddddddDDDDDDdddqllqllllllllllllqddddqqppddddDDDDDDDDDDDDDdddddddrdrdddddddddddDDDDDDDDdddddddddddddddddpdpppppppppppggggghgghhphhhhaawaaawaawwww^^^^wwww^^^^^!!!^^^^^!!!^^^^^^^^iiiddddriiddddddddDDDDDddddqlllllqdqqrlllqrddddDDDDDDDddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssqsssssssqaaaaaaaaaaaawwaaaaaaaaaaaaaaaaaaaaaaaaaaaawwwwwwww^^^!^^^^^^ddddddddddDdddqs~~~~~~~~sqdqs~~ssqqddddddddddddddDDDddd^^^ddqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddddddddddddDddrRRggggggggggggggggggggrggggggggggggggg^^^^^dddddddDDDdddddddddddqllllllllllqqllqqdddddddDDDDDDDDddqlllllllllllllllllqqqqlqpdddDDDDDDDDDDDDDDDDdddddddrrrdddddddddddDdDdDDDDdDddddddddDDdddddddpppppppppggggggggghhphhhhhaaaawaawwww^^^^wwwwww^^^^!!^^^^^^^^^^^^^^^iiiiiddddridddddddDDDDddddddqlllllllqlllllllrqddddDDDDDDddddqs~~~~~~~~~~~~~~~~~~~~~~sqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssssssqqssqaaaaaaaaaaaaawaaaaaaaaaaaaaaaaaaaaapaaaaaa^wwwwww^^^^!^^^^^^ddddddddDDdddddqs~~~~~~~~sqs~~~~sssqqddddDDdddddDDdd^^dd^dddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddDDDdddDdddDDdddrRrgggggggggggggggggggrgggggggggggggg^^^gggddddddddddddddddddddqlllllllllqddqqddddddDDDDDDDDDdddddqlllllllllllllllllllllqddddDDdddddDDDDDDDDDDDddddddddrrrddqddddDDDDDDDDDDDDDDDddDDDDDdddddpddpppppppppgggggghhhhghhhhaaawwaawww^^^!^wwwwwww^^^^^vvvvvv^^^^^^^*riiiidddddrdddddDdDDDDdDddddqllllllllllllllllllqdddDdDDDDddddqs~~~~~~~~~~~~~~~~~~~~~~qdddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqqqqdpqsqppaapaaaaaaaaaaaaaaaaaaaaaaaapaaapppapaaa^^^ww^^^^^^!!!!!^^^ddddddDDDDdddddqs~~~~~~~~~s~~~~~~~~ssqddddDDddDdDdd^^^^dddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddDDDDDDdDDDDDddddrRrggggggggggggggggggrggggggggggrRRrg^^ggrrrrrrddddddddddddddddqllllllllqddddddddDDDDDDDDDDDDdddddqlllllllllllllllllllllqddddDddddddDDDddDDDDDDDDdddddddrrrlqdddDDDDDDDDDDDDDDDDdDDDDdDDddddddppppppppppgggggghhhpahhhhaaawwwwwww^!^^^w^^ww^^^^^^vvvvvvv^^^^^^^rrrrdddddrddddddDDDDDDDDDdddqlllqqllllllllllllllqdddddDDDDdddqss~~~~~~~~~~~~~~~~~~~~~qdddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddpddqssqpppaapaaaaaaaaaaaaaaaaaaaaapappdppdpaaaa^^^^^^^^^^^!!!!^^^dddddDDddDDddddqs~~~~~~~~~~~~~~~~~~~~sqdddddDDDDDDd^^^^^^^dddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qddddddDDDDDDDDDDDDDddddRrgggggggggggggggggggrggggggrRRRRRRRRRRRRRRRRRrddddddddddqqdqqlllllllllqdddddddddDDDDDDDDDdddddddqlllllllllllllllllllllqdddddddqqdddDDddddDDDDdDDDdddddddqllqddDDDDDDDDDDDDDDDDDDDDdDddddddddppppppppppggggggghgppaagaagaawwwwww^^!^^w^^^^^^^^^^^vvvvvvv^!!^^^ddddrddddrddddDdDDDDDDDDddhddqqqppqllllllllllllllqddddDDDDddddqq~~~~~~~~~~~~~~~~~~~sqddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqddddddqssqqddpppaaapaaaaaaaaaaaaaaapaappdddpppppaa^^^^^^^^^^^!^!!!^^ddddDDDDdDDDdddprs~~~~~~~~~~~~~~~~~~~~~sqqdddDDDDDDdd^^!^^^^ddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddddDdDDDDDDDDddddddddRrggggggggggggggggggrrrRRRRRrpp^^^prrRrpddddrRrddddddddqllqlllllllllllqddddddddddDDDDDDddddddddddqllllllllllllqqlllllllqdddddqllqdddddddddddddddddddddddqllqdddDDDDDDDdDDDDDdDDDDDDDDdddddddppppppggpggggggggggpaagggagawaaawwa^^^!^w^^^^^^!!^^^vvvvvvv^^^!^^dddddrrrrddddDDDDDDDDDDDddhddddpppqllllllllllllllqddddDDDDDdddddq~~~~~~~~~~~~~~~~~ssqddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~~~~sqdddddqsqdddddpppppaapadaaaaaaaaaaaappppddpppdddpd^^^^^!!!^!!!^!!^^ddddDDDDDdDddddrrdqs~~~~~~~~~~~~~~~~~~sssssqqddDDDDdd^^^!!^^^dddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~sqdddddDDddddDDDDDDDDDDdddrRrggggggggggggggggggrRrrrrppp^^^^^ppppppddddrRrdrrrrrrllllllllllllllqdddddddpddddDDDddddddddddddqlllllllllqqqddqlllllllqqdddqlllqddddqdddddqqdddddddqqqllqddddddDDddddddddddDDDDDDDDddddpdppppppggggggggpgggggppaggghgaaaaawaaaa^!^ww^^^^!!!^^^^^vvvvv^!!!^^ddddddddrdddddDdDdDDdDDDddddhhhpdppqllllllllllllqdddDDDDDDDddddddq~~~~~~~~~~~~~~~sqqddDdddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~ss~~sqqs~~~~~~~~~~~~sqddqqssqdddddddddppppddadaaaaappppppdpppppdddddddd^^^^^!!!!!^!!!^^^ddddddDDdddddrddpqs~~~~~~~~~~~~~~~~ssqqs~~sqdddDDdd^^^!!!^^ddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqsss~~~~sqdddDDDDddddDDDDDDdDDDdddgrRgggggggggggrrrrrrrRrpppppp^^!!^^ppprrrrrrrRRRRRRRRRRlqqqlllllllllllqqqdddpqdddddDddddddpdqqddqlllllllllqdddddqqlllllllqddqllllqdddqlqdddqllqddddqdqlllllqdqdddDDdddddddddddDDDDDDddddddpppppppggggggpggpgggggpgggghhpaaaaaapaa^^^ww^^^!!!!!^^^^^vv^^^^!^^ddDDdddddrddddDDDDDDDDDDDDddddhhhpdppqlllllllqqqqdddDDddDddddddddddq~~~~~~~~~~~~~sqddddDdDDdq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~sqqssqddqs~~~~~~~~~~~~sqqsssqdddddddddpdppddddaaapappppppddddppddpddddddd^^^^^!!!!!^!!^^^^^^dddDDddddrdddddqs~~~~~~~~~~~~~~sqqddqs~sqddddDd^^!!!!^^^ddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~ssqddqqqs~~~~sqddDdDDdddDDDDDDDDDDddddggrRrggggggrRRRRRRRRRRRrpppp^^^!^^^pprRRRRRRRRrrRggggggqgggqlllllllllllllqqqqqdddddddddpdpdqllqqlllllllllqqdddddddqlllllllqqllllllqqqlllqqqllllqqqqlqlllllllqlqdddddddddddddddddDDdddddddppppppppgpppppppppggggggggghhhhpaaaappaa^^www^^^!!!!!^!^^^^^^^^^^^ddDDDdddddrdddddDDDDDDdDDDDDDDhhhhpppqllllqllqdddddddDdddddddddddddq~~~~~~~~~~~~~sqdddddDdDDddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~sqddqsqdddqs~~~~~~~~~~~~~s~ssqddDDDdddddddppdddddaapdpppdddddpddddddddDddddd^^^^^!!!^!^!!^^^^^ddDDddddrddddddq~~~~~~~~~~~~~sqdddddqssqdddddd^^!!^^^^ddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqqqqsssqqdddddqsssssqddddddpdddDDDdDDdddddggdggrRRRRRrrRrrgggggggrrRrrppp^^^^^pprRRggggggrggggggggggggggqlllllllllllllllllqqqdddddddpqqllllllqqqlllqqdddddddddqllllllllllllllllllllllllllllllllllllllllllllqddddddrrrrrrdddddddddddpppdppppppppppppppgggggggggggghhppapppapaaw^ww^^^!!^!!!!!^^^^^^^^^^^ddDDDdDddddrddddDDDDDDDDDDDDDDddhdddpqlllqpqqddddddddddddddddddddqq~~~~~~~~~~~~~~sqdddDDDDDDdddqs~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~sqdddqssqddq~~~~~~~~~~~~~~~~~sqddDDDDDddddddpppddpapddddppddddddddddddDDdddddd^^^!!^!!!^!!^^^^dddddddddrddddddqs~~~~~~~~~~~~~qddddddqssqpddddd^^^!^^^dddqs~~~~~~~~~~~~~~~~~~~~~~~sqqssqqqddddqqqddddddddqqssqdddddddddddddddDDDdddggggggggrrrRRRrgggggggggggrRRrrppppppprRrggpggggggggggggggggggggqqllllllllllqqlllllqddddddqqqllqqllqdddqqqdddddDDddddqqqllllllllllllllllllllqqqllqqqlllllllllllllqddqqdrrRRRRRRRrddddddddpdpdddpppppppppppppppgggggggggghggppgpappaaaww^^^!^^^!!!^!!!^^^^^^iiiddDDDdDdDDdrddddDDDDDDDDDDDDDDDDdddddqllqppqdddddDDDddddddddddddq~~~~~~~~~~~~~~~~sqddddDDDDDddddq~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~sqddddqssqqs~~~~~~~~~~~~~~~~~ssqddddDDDDddddpppaaapdpdddddddddddddDDDDDDDdddqqll^^^^^^!!!!!!^^ddddddddrdddddddq~~~~~~~~~~~~~qddDDddddqsqdddddd^^^^^dddddq~~~~~~~~~~~~~~~~~~~~~sssqddqqddddddddddddddddddddrrdddddddppdddddddDDDddgddggggggggggggggggggggggg^ggpRRrrprrRRRrppppppggggggggggggdgggggggqllllllllqddqlllllqqdqqqllllqddqqddddddddddddDDDddddddqlllllllllllllllllqqdddqqgggqlllqqqlllllllqqllrllrrddddrRrrddddddddppdpppppppppppppppgggggggggggggggggaappaaww^^^^^^^^^!!^!!!^^^^^iidddDdDDdDDDddrddddDdDDDDDDDDDDDDDDddddddqqppddddDDDDDddddddddddddq~~~~~~~~~~~~~~~~~qddddDDDDDDDdddq~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~ssqqdddq~ss~~~~~~~~~~~~~~~~~~~ssqddddDDDdddddpppppddddddddddddddddDDDDdDddddqllllll^^^^^!!!!!^^ddddddrrrddddqqs~~~~~~~~~~~~~sqddDDDDdqssqddddddd^^dddddqs~~~~~~~~~~~~~~~~~ssssqqqddddddddddddddddddddddddddrddddddpdpddddddpddDdddddgggggggggggggggggggggg^^^ppprRRrrRrppppppppgggggppggggddddggggggqlllllqqqdddqlllllllqllllqqllqddddddddddddddDDDddddddddqlllllllllllqllqqddddddggggqlqqgggqllllllllllllrddddddddRRRdddddddddppppppppppppppppgpgpgggggggggggggppppaaap^^^^^^^^^^!!!^^^^^^iiidddDDDDDDDDddrdddDDDDDDDdDDDDDDDDdDddddddppdddddDDDDddddddddqdqqq~~~~~~~~~~~~~~~~~sqddDDDdDDDDDdddqs~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~sqdqs~~~~~~~~~~~~~~~~~~~~~~~ssqdddDDDdddddddppddpddddddDDdDddddDDDDDDdddqllllllll^^^!!!!^^^^^dddrrdddrdqqss~~~~~~~~~~~~~~~sqddDDDddqsqddddddd^^ddddqs~~~~~~~~~~~~~~~~sqqqqqddddddddddddddddddDDDdddDdddddrdddddddpddddppppdddddggggggggggggggggggggggggg^^p^^pppRRppppppppppppggppggddddddgggdggdqlllqqdddddddqqlqqqlllllqddqllqddddddhddDDDDddddddddddddqlllllqqqqqdqqddddddddgggggqggggggqllllllllllqqddddddddrrRrrrdddddddpppppppppppppppppppggggggggggpgppppppppp^ii^^^^^^^!!!^^^iiiidddddddDdDDDDDdrddddddddDDdDDDDDDDDDdddddddddddddddDDDDDDddqqqsqss~~~~~~~~~~~~~~~~~~sqddDDDDDDDDDDDqss~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~sqs~~~~~~~~~~~~~~~~~~~~~~qqqssqdDDDDDDDddddppddddddDdddDDDDddDDDdDDdddqllllllllll^^!!!^^^^^^ddrddddddrqss~~~~~~~~~~~~~~~~sqdddDDddqsqdddddddddddqqs~~~~~~~~~~~~~~~~sqdddddddddddddddDDdddddddDDDdDDDDdddrdddddddpppddpppdddddddggggggggggggggggggggggggggg^^^^ppppppppppppppppppdddddDDddgdddggddqqqdddddddddddqdddqlllqdddqlqddddhdhhddDDDdddddddddddddqllllqdddddddddddddDDgggggggggggggqlllllllllqddddddddddddrRRRRrrdddppppppppppppppppppgppggpgggggggpppppppppppiiiii^^^^^^!^^^iiiddddddddddDDDDDdrdddddddddddDdDDDDDDDDddddpdddddddddDDDddddqsss~~~~~~~~~~~~~~~~~~~~ssqqddDDDDDDDDDDddqs~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~sqqs~~~s~~~~~~~~~~~~~~~~~~~~~~qdddqssqdddDdDDDdddddddDdDDDdDdDDDDdDDDdDddddqqllllllllll^^^!^^^^rrrrrddddddddrsss~~~~~~~~~qqqss~~sqddddddqssqqqqdddddddqss~~~~~~~~~~~~~~sqqdddddddddDDdddDDDddddpdddDDDDDDDDDddrdddddddppppppddddDdddgggggggggggggggggggggggggpp^^^^ppppppppppppppppppppddDDDDdgggdddddddddddddDDDdddddddddqlllqqdqlqddhhhdhhddDDDdddqqqqdddddddqllqdddddddDDDDDDDDDDDggggggggqqqlllllllllllqddddddddddddddyrRRrrrpppppppphppp^ppppppppppppgggggggpppppppppppiiiii^^^^^^^^^iddddddpddDDDDDDDDddrddddddddddddDDDDDDDDdddppppddppdddDddddddqs~~~~~~~~~~~~~~~~~~~~~sqqdddddDDDDDDDDDddqs~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~sqddqs~~~~~~~~~~~~~~~~~~~~~~~~~qdddqsqddddDDDDDDddddddDDddDDDDDDDDDDDDDddddqllllllllllll^^^!^!^^^^ddddd^^d^dddqqss~~~~~~sqdddqss~sqdddddqsssssssqqqddddqs~~~~~~~~~~~~~~~qddddddddddDDdDdDdDddddppddDDDDDDDDDdddrddddddpdpppdpddddDddddggggggggggggggggggggggggppp^^^ppppppppppppppppppppdddDdddggdgdddddddddddDDDDDDdddddddqlllllqllqdhhhhddddDDddddqllllqddqqqqllqdddDDDddDDDDDDDDDDggggggggqlllllllllqlqllqdddddDdddddddyyyyrRRRRryyppppppp^^ppppppppgggppgggggpggppppppppiiii^iii^^^^^iiidddddpdddddDDDDDDdddrddddddddddddDDDDDDdddddpppdppppddDdddddqss~~~~~~~~~~~~~~~~~~~~~qddddddDDDDDDDDDdddq~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~sqdddqs~~~~~~~~~~~~~~~~~~~~~~~~~~qddqssqddDDDDDDddddddDDDDDDDDDDDDDDDDDddddqllpqlllllllq^^^^^^!^^^^^^dd^^^^^^ddddqsss~~~sqdddddqs~~sqdddqssssqs~~sssqqqdqs~~~~~~~~~~~~~~~qdddddDddDDDDDDDddddddpdppddddDDDddDDdddrrddddppppppddddDDdddggggggggggggggggggpggggpppp^^ppppppppppppppppppppppggdddgggggggddddDDDdDdDDDdDDDdddddqllqlllllqddhhhddddDDDdddqllqqllqqlllllllqdddDDdDDDDDDDdddDDdggggqqllllllllqqgqdqllqdDDDDdddddyyyyyyyyyyrRryyyypppp^^pp^^^pppgppggggggggggggpppppiiiii^^^i^^^^iiiidddddddddddDDDDDDddddrrddddddddDDDdDDDDDdddddddppppdddddddddqs~~~~~~~~~~~~~~~~~~~~~sqddddddDDDDDDDDDDddqs~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~sqddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~qqsssqdddDDDDDddddddDDDDDDDDDDDDDDDDDddddqllqlllllllqddd^^^^!!^!^^^^^^^^^^^ddddqqqssssqddddddqs~~sqddqsssqqpqs~~~~sssqs~~~~~~~~~~~~~~~~sqqdddDDDDDDDDDDddDddppppppdddddDDdDDDddddrdpdpppppppddDDDddddddgggggggggggggggppppppppppppppppppppppppppppppggggggddggggggdddDDDDDDDDDDDddddddddqllqdqlllllqddhhddDDDDDddqllqddqlllllllllllqddDDDddddddqdddddddgqqllllqllllqgggddqqqdddDDDdddddddyyyyyyyyyrRryyyypppppp^^!^^pppppgpggggggggggg^^p^^^ii^^^^iiiiiiiippddddpddddDDDDDDDDDddddrrrdddddddDDDDDDDDdddddpdppddddddddddqs~~~~~~~~s~sqqs~~~~~~~sqdddDDDdDDDDDDDDddqss~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~sqqddDddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqdddDdDdDDDDdDddDDDDDDDDDDDDDDddDdddqllllllllqpddd^^^!!!!!^^!!^^^^^^^^ddddddqqqqqdddddddqs~~sqqs~sqpppqs~~~~~~~~s~~~~~~~~~~~~~~~~~ssqdddDDDDDDDddddDddpppppppddddddddDDDdddrdppppddpdpddddDddddpdgggggggggggggggggpppppppppppppppppppppppppppppppppggggggggddddddDDdDDDDDDdddddqqqllqddqlllllqqddhddddDDDddqlqddqlllllllllllqqdddDdddddqqlqqdddqqglllllqgqlllqgggdddddddDDDDddddddyyyyyyyyyyyrRRyyyypppp^^!^^ppp^pgggggggg^^g^^^^^^^^^iii^^^iiiiiipppppddpppdddDDDDDDDdddddddddrrrdddddDDDddDDdddddddpddddddddddqs~~~~~~sqqqsqddqsss~ss~ssqddddDDDDDDdDDddddqs~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~qdddDDddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddDDDDDDDDDDDDDDDDDDDDDdDdDddddqllllllllqdd^dd^^^!^!!!^!!!^^^^^^^^dddddddppddddpdddqs~~~~~~~~sqppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddDDDDDDddDDddpppdddddddddppdddDddddrppppdddddddddDdddppggggggggggggggggggpppppppppppppppppppppppppppppppppgggggggggdddddDDDDddDDDdddqqllllllqqlllllllqddddddddDDddqllqdqllllllllllqddddddddddqlllllqqqlllllllqggqllllqddddddddDDddDdddddyyyyyyyyyyyyyrRryyyppppp^^pppp^^^ggggggg^^^^^^!!!!^^^iii^^^^iiiipppppdddddppddDdDdDDDDdddddddddddrdddddDDdddDDdddddddddddddddqdq~~~~~~sqdddqqdddqqqsqqssssqddddDDDDDdDDDdddqs~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~sqdddDDdqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddDddDDDdDDDDDDDDDDDDDDDDDdDDDddqlllllllllqdd^^^^^^^^^!!!!!!!^!!^^^^DDDdddddddddddddddqs~~~~~~~~sqpq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qdddddddDDDDdDDDDdppddddddpppdpppdddddpprpppppddddddpdddddppgggggggggggggggpgpppppppppppppppppppppppppppppgggggggggggggdgggdddDDDddDDDddqllllqqqllllllllllqdddddqddDDdqllllqlllllllqllllqqddqddddqllqllllllllllllqggggqllqddddddDDDDDDdDdddyyyyyyyyyyyyyyyyRRryyyppppppp^^^^^^^ggggg^^^^^!!!^!!^^^ii^^^^^iiiippppddpddpddddDDdddddddddddddddddrdddddddddddddddddddddddddqqsq~~~~~~ssqdddddddddddqddqs~~qddddDDDDDDDDDddddqs~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~sqddDDDDddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddDdDdDDdDDDDDDDDdDdDDDdDDddqlllllllllqdd^^^^^^^^^^!!!!^^!!!!^^^^DDDDDddddddddddddddqss~~~~~~~sqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddDDDDDDdddpdppppdddppddppddddddpprrppdddddddddddppdpggggggpgggggggppppppppppppppppppppppppppppppggpppgggggggggggggddddddddddDDddqqllqdddqllllllllllqdddqlqdDDddqllllllllllqdqlllllqqlqqqqllqdqllllllllllqqqggggqqdddDddDDDDDDDdDddddyyyyyyyyyyyyyyyrRRpyyyyyppp^^^!!!!^^g^^^^^^!!!!!!^^^iii^^^^^^iiipppppddpdpddpddddddddpdddpdpddddddrdddddddddddddddddddddddddqs~~~~~~sqqqqddddddDDddddddqs~~qdddddDDDDDDDDDDddqq~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~qddDDdddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddddddDDDDDDDDDDDDddDDddDddqllllllllqdd^^!!!^^^^^^^!^!!!!!!^^^^^^^^DDDdddddddddpddddqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqddddddDDDDDddddddpppddddppppddddddppppprpppddddddddpppppgggggggpppgggpppppppppppppppppppppppppppppgggggggggggggggggggggggdddddddDDddddqlqddqlllllllllllqddddqlqddddqllllllllllqdqlllllllllllllqddqlllllllllqdgggggdddddDdDdDDDdDDDdDddddyyyyyyyyyyyyyyyyrRryyyyyyppp^^^!!^^^^^^^!!!!!!!!^^^iii^^^!^^iiiiipppppddpppddddddddppdddpppddddddddrrddddddddddddddddddddddqs~~~~~ssqddddDDDDDDDDDddddqs~~~~qqdddDDDDDDDDDDDdddqs~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~sqddDDddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqdddddddddddDDDDDddDDddDddddddqllllllqdd^^^!!^^^^^^^^!!!!!!!^^!^^^^^^^^DDddDDd^dddddddddqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddddDDDdddDdddpppdppdpppppdddpdpppppprpppppddddddpppppgggggpppppgggppppppppppppppppppppppppppppppggggggggggggpggggggggddddddqdddddqqllqdqlllllllllllqddddqllqdddqllllllllllllqllqqqlqqqllllllqqllllllllqllqdddddddddDDDDdDDDdDdDDddydydyyyyyyyyyyyyyyyyrRrryqqyppppp^^^^^^^^!!!!!^!!^^pppi^^^^!!^^iiiiipppppppppppdddddddpppdddppddddddddddrqdddddddqqdddddddddddqs~~~~~sqdddddDDDDDDDDDDddqs~~~~~qddddDDDDDDDDDDDddddqs~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~sqdddddqddq~~~~~~~~~ss~~~~~~~~~~~~~~~~~~~~ssssqqdddddddDDdddddddddDDDDdDddqlllllllqdd^^!^^^^pp^^^^^!!!!!!!^^^^!^^^^^DDDDDd^^ddddddddddqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddDDDDDddDDddpppppppppppddddpppppppprppdpdddppdpdppppggggggppppggppppppppppppppppppppppppppppppgggggggggggggggggggggggddddqlqdddqlllllqlllllllllllllqddqllllqqqlllqqqqllllllllqdddqdddqllllllllllllllqgqqddddddDDDDdDDDDDDDDDDDDdddydddyyyyyyyyyyyyyyyyrRRrrsqyypppppppp^^^^^!^^^^^^pppppp^^^!!^^^^^iiippppppppppddpdddddpdddppddddddddddqssqqdqqqqssqqdddddddddqs~~~~~sqddddDDDDDDDDdDDddqss~~~~~qddddDDDDDDDDDDDDdddqs~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~sqddddqqq~~~~~~~~ssqqqs~~~~~~~~~~~~~~~~~~~~~sssqdddddddddddddddddDDDDDddddqllllllqpdp^^^^^ppppp^^^^!!!!!!^^!!!^^^^^^DDDD^^^^dddddddddddqqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddDDDDDDDdDDDdddpppppppdppddddppdpppprddddddddpppppppgggggggppppggppppppppppppppppppppppppppppppgggggggpppggggggggggggddddqllqddqllllllllllllllllllqllqqlllllllllqqddddqlllqqqqdddddddqllllqlllllllllllqdddddddddDDDdDDDDDDDDDDddddydddddyyyyyyyyyyyyyyyrRRRrssqyypppppppp^^^^^!^^ppppppppp^^!!!^^^^^^^ipppppp^^ppppppdddppppppppddpddddddqssssqsss~~ssqddddddddqs~~~~~sqddddDdDDDDDDDDDDDddqqs~~~~~qddddDDDDDDDDDDDDddqs~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~sqdddqsss~~~~~~ssqqdddqs~~~~~~~~~~~~~~~~~~~~~~~sqddddddddddddddddddDDdddddrrllllllqqpp^^pppppp^^^^^^!!!!!^!!^!!^^^^^^DDD^^^^^ddddddddddddpq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddDdDDDDDDDDDddddppppdpddddDDddpppppdrdddddddddddpppgggggggggppppgpppppppppppppppppppppppppppppgggggggppppggggggggddgggddqllllqdqlllllllllllllllllqdqlllllllllqqqddddddqllqdddddDDdddqlllqqdqlllllllllllqddddddhhDDDDDDDDDdDDDDdddddyydddyyyyyyyyyyyyyyyrsrRssssqyyyypppppppp^^^^ppppppp^^^^!!!!!!!!^^^ippppp^^^ppppppddpppppppppppdddddddqss~ss~~~~~~~sqqddddddqs~~~~~~sqddDDDDDdddDDDDDDddddqs~~~~sqdddDDDDDDDDDdddddqssss~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~sqqqs~~~~~~~~ssqddddddqs~~~~~~~~~~~~~~~~~~~~~~~sqqdqqqqqqddrrdddddddddddRRRrlllllllqpppqqpqqp^^^^^!!!!!^!!!!!!^^^^^^^^^^^^^^^ddddddddddpppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqdddDDDDDDDdDDddddpddppddddddDDdddppdddrddddddddddddppgggggggggppppppppppppppppppppppppppppppppppggggggggppppggggggddddddddqlllllqllllllllllllllllllqddqqqlllllqddddhhhdddqllqddDDDDdddqllqddddqlllllllllllqddddhhhhDDDDDDDDddDDDddddddyyydyyyyyyyyyyyyyyyqssrssssqyyyyyyppppppp^^^pppppp^^^^!!!!!^!^!!^^ipppp^^!^^^^pppppppppppppppddddddpqss~~~~~~~~~~~~sqdddddqs~s~~~~~sqdDDDddddddddddDDddddqs~~~~~sqddDDDdddDDDddddqsssqqqs~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~sss~~~~~~~sqqssqddDdddq~~~~~~~~~~~~~~~~~~~~~~~~ssqssssssrRRRRrddddddrrrRrddqlllllllqpqllqll^^^^^!!!!!!!!!!!^!!^^^^^^^^^^^!^^ddddddddd^pppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddDDDDDDDDDDdddpdddpppddddDDDddppppddrdddDDDdddddddpppgggggggpppppppppppppppppppppppppppppppppggggpggggpppppgggddddddddddqlllllllllllllllllllllllqddddddqlllqdddhddhhddddqlqddDDDDddddqqddddqlllllllllllllrrddddhhDDDDDDDDDDDDddddddyyyyyyyyyyyyyyyyyyyyqssrsssssqyyyyyppppppppppppppp^^^^^^!^!!!!!^!^^ppp^^^^!^^^^^ppppppppppp^pddddddppqs~~~~~~~~~~~~~~sqddddqsss~~~~~sqdDDdddqqqqdddddDDddddqs~~~~sqdDDDddddddDDdpppqqqpppq~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~sqddqssqdDDdddq~~~~~~~~~~~~~~~~~~~~~~~~~s~~~sssRRddRRRrrrrRRRRrdddqllllllllqllllll^^^^^!!^^^!!!!!^^!!^!^^^^^^^!!!!^^dddddd^^^ppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqsqddddDDDDDDDDdDDddppdppdppppdDDDdddddpdddrddDDDDdddddddppppggggggppppppppppppppppppppppppppppppppgggggpgggggppppggdddddDdDdddxqlllqqqqllllllllllllllqdddddddqqllqddhhhddhddDddqddDDDDDDDDddddddqlllllqqlllllllqdrrdddhDDDDDdDDDDDDdddddddydyyyyyyyyyyyyyyyyyyqssssssssqyyyyyppppppppppppp^^^!^!!!^!!^!!!!!^^pppp^!!!!!!^^ppppppp^ppppdddddppppqs~~~~~~~~~~~~sqddddddqs~~~~~sqddddddqssssqqqqdddddqqs~~~~~sqdDDDdddddddddpppppppppqs~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~ssqdddqssqdDdqqs~~~~~~~~~~~qssss~~~~~~~~~~~~~~~~srdddrdRRRRrddrdddqllllllllllllllll^^^^^^^^^^^!!^^^!!!!!^^^^!^!!!^!!^^ddd^^^^^^ppppqss~~~~~~~~~~~~~~~~~~~~~~~~~sqdqddddDDDDdDDDDdddddppppddppdpdddDdddddddddrdddDDDddddddddpppgggggpppppppppppppppppppppppppppppppppppggppggggpppppggdddDDDDDddxSqllqSSSSqqlllllllllllqdddDddddddqllqdddddddDDDddddDDDDDDDDDdddddddqlllqddqqllllqqdddrddddDDdDDDDDDDdddddddddyyyyyyyyyyyyyyyyyyyqsssssssssqyyyyyyyppppppp^^^^!!!!!!^!!!!!!!!!^^^^pp^^!^^^!!^ppppp^^^^^ppppddpppppq~~~~~~~~~~~~~sqddddddqs~~~~~~sqdddddqs~~~ss~sqdddqss~~~~~~sqddDDdddddpdddpppppp^^ppqs~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~ssqdddddqsqdddqs~~~~~~~~~~sqdqssqqss~~~~~~~~~~~~~ssqdpdddddddddrddddqllllllllllllllqi^^^^^^^^^^^^^^!!!!!!!!!!!!!!!!!!!^^^^^^^^^^^ppppqqs~~~~~~~~~~~~~~~~~~~~~~~~sqddddddDDDDdDDDDdddddddppdddddpddDdDdddddddrdddDDDDdddpppdppppggggpppppppppppppppppppppppppppppppppppppgpppppggppppgdddddDDDDdxSSSqlqSSSSSSqlllllllllqdddDDDddddddqllqqddDDDDDDDdddDDDDDDDDDDDdhdddqllqdddddqllqddddddrdddddddDdDDDDddddddddyyyyyyyyyyyyyyyyyyyyqssssssssssqqyyyyyyypppppp^^^!!!^!!!!!!!!^!!^^^^^pppp^^p^^!^^pp^^^!!^pppppppppppqs~~~~~~~~~~~~~sqddddddqss~~~~~~sqqqqqs~~~~~~~~sqdqs~~~~~~~sqdddDDdddpddpddpppppp^^ppqss~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~sqqdddDddqssqqqs~~~~~~~~~~~~sqssqddqqs~~~~~~~~~~~~sqdddDddDDddddrddddqqlllllllllllqqii^^^^^^^^^^!^!^!!!!!!!!!!!!!!!^!!!^^^^^^!!^^^^^ppppqq~~~~~~~~~~~~~~~~~~~~~~~~sqddddddDDDdDDDdDddddddpppddddddDDDDddddddrddddDdDDddddppppppppggpgpppppppppppppppppppppppppppppppppppppppppppggpppddddddddDdddxxSSrSSSSSSqlllllllllqddddDDDddddqqlllllqddDDddddDDDDDDDdDDDdDdddddddqllqdddddqqddddddddrrddddddDdddDdddddddyyyyyyyyrrryyyyyyyyyyyqsssssssssssqqyyyyypppppppp^^^^^^!!!!!!!^!!!!!^^^pppppp^^^^^pp^^!^^^pppppppppppqs~~~~~~~~~~~~~~sqddddddqs~~~~~~~sss~s~~~~~~~~~~sqs~~~~~~~~qdddDDDddddpdpppppppp^^^^ppqq~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~sqddddDDdddqsss~~~~~~~~~~~~~ssssqdddddqs~~~~~~~~~~~sqdddDDDDddddrddDddddqlllllqlllqppiiiii^i^^^^^!!!^^^!!!!!!!^!!!!!!!!^!!^^^!!!!!!^^ppppppq~~~~~~~~~~~~~~~~~~~~~~~sqdddddddDDDDDDDdDDdddddpppddddDDDDDddddrRddddDDdDDdddddpppppppgppppppppppppppppppppppppppppppppppppppppppppppppppddpddpdddDDdxxSSSrSSSSSSqllllllllqddddDDDddddqllllllqddddddddddDDDdDDddDDDDDddddddqlqddddddddddddddddddrrrddddddddddddddyyyrrrrrryyyrryyyyyyyyyqssssssssss~ssqqqyyppppppppp^^^^^^!!!!!^^!!!!!^^^^^ppppp^^!^^pp^^^pppppppppppppq~~~~~~~~~~~~~~~~sqdddqqs~~~sqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~qdddDdDddddppppppppp^^^!^ppppq~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~sqdddDDDDdddqss~~~~~~~~~~~~~sqqssqddddddq~~~~~~~~~~~sqddddDDddddrddDDDDddqllllqdqlqddppiiiiiii^^^^^^^^^^^!!!!!!!!!!!!!!!!!!^^!!!!!!^^^ppppppq~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddDDDDDDDDddddddddddddDDDDDddddrRddddDDDDDDDdddddpppppppppppppppppppppppppppppppppppppppppppppppppppppppppppddpddddDDdddxSSSrSSSSSSqllllllllqqdddDDddqqllqqllllqqdddqqqqdddDDDdddddDddddddqqlllqdddddddddDdd^dddddddrdddddddddddddrrryyyyyyyyyyyryyyyyyqqsssssssss~s~~ssssqqyppppppppp^p^^^^!!!^!!!!!^!^^^^^pppqpp^^^^ppp^^^pppppppqqppqs~~~~~~~~~~~~~~~~~sqqqss~~~sqdqs~~~~~~~~~~~~~~~~~~~~~~~~~~~qdddddddddppppppppp^^^!!^^ppppq~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~qdddDDDDDDdddqs~~~~~~~~~~~ssqddqssqddddddq~~~~~~~~~~~sqqdddddrrrddDDDDDdddqlqqddqqddddpiiiiiiii^^^^^^^^!!!!!!!!!!!!!!!!!!^^!!!!!!!^^^^ppppppq~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddDDdDDDDDddddddddDdDDDDdddddrRrdddDDDDDddDdddddppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppdpddpddDDddxxSSrSSSSSSqllllllllllqdDDddqlllqddqlllllqqqllllqdddDDdddddddddddqllllllqqdDDDddDDD^^ddddddddrrrddddddrrrrpyyyyyyyyyyyyyyrryyrrsssssssssss~~~~~~~ss~qqqqpppppppppp^^^!!^^^^!!^!!^^pppqqsqpp^pppppp^^pppppqqssqqs~~~~~~~~~~~~~~~~~~~~ss~~~ssqdddqs~~~~~~~~~~~~~~~~~~~~~~~~~~sqqddddddqppppppppp^^!!!^^^pppqs~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~sqddDddDDdddgqs~~~~~~~~~~ssqdddqsqdddqqqqss~~~~~~~~~~~ssqdqdrdddddDDDDddDddqddddDdddddpiiiiiiii^^^^^!!!!!!!!!!!!!!!!!!!!!!^^!!!!!^^^pppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddDDDDDDDDDddDdddDDDDDDDddddrRrdddDDDDDDddddddddppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppdddDDdddxxSSrSSSSSqllqllllllqddDDdddqqllqddqllqlllllllllqqddDdddqqqddddqllqllllqddDDDddDD^^^^Ddddddddddrrddrrpppppppyyyyyyyyyyyyyyrryyqsssssssss~~~~~~~~~~~ssssqqpppppppp^^^^^^^^^!!!!^^pppqssqpppppppppppppppqqss~~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~qdddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddqsqppppppppp^^!!!!^^pppqss~~~~~~~
~~~~~~~~~~~~~~~~~~~~~sqdddddddddggqs~~~~~~~~~~sqdddqssqdqsssssqqqss~~~~~~~~ssqsrqdddDDDDDDDDDddddddDdddddpppiippii^^^^^^!^!!!^^^!^!!!!!!!!!!!^!^!!!!^^^ppppppppq~~~~~~~~~~~~~~~~~~~~~~~~~sqddqdddddDDDDDDDDDdDDDdDDDDDDDDdddrRrddddDdDdDdddddggdpppppppppppppppppppppppppppppppppppppppppppppppppppppppppppggpdpdddDDDDdxxSSSSrSSSSSrqdqlqlqqdddDDdddddqllqdqlqdqqlllllllllqddddqllqddqqllqdqlllqdddDDdDDD^^!^DDdDDdddddddrrppppppmmppyyyyyppyyyyyyyyyyqsssssss~~~~~~~~~~~~~~~~~ssqppppppppppppp^^!!^!^^^pppqsssqqpppqqpqqqqqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqdqqssqppppppppp^^^!!^^^^pppqq~~~~~~~
~~~~~~~~~~~~~~~~~~~~~ssqddgddgggggqq~~~~~~~~~~~sqdqssssqssqqqqdddqqs~~~~~~~~~~ssqdddDDDDDDDDdDDdddDDdddddpppppppii^^^^^^^^^^^^^^^^!!!!^!!!^!!!!!!!^^^^^ppppppqqs~~~~~~~~~~~~~~~~~~~~~~~~~~sqqsqdddddddDDDDDDDDDDDDDDDDDDDdddrRddddDDddDdddddggggppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppgggdddDDDDDddxxxSSrSSSSrSxdqqdqddddDDDdddddqlllqllqdddqlllllllllqqqqllllqqlllqdddqqllqddDDDDDD^^!^^DDdDDddddddddddpppmmmppyyypppppyyyyyyyyyqssssssss~~~~~~~~~~~~~~~~~sqppppppppppp^^^!!!!^^^^ppqss~~ssqqqssqssssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~q~~~sqpppppppppi^!^!^^^^pppppq~~~~~~
~~~~~~~~~~~~~~~~~~~~~~sqddggddggggggq~~~~~~~~~~~sqs~~ssssqdddddddddqss~~~~~~~~~~sqdDDDDDDddddddDDDDDddddpppppppppx^^^^^^^^^^^^^^!!!^^!!!!^^^^^!!!^^^^^pppppqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqdddddddDDddDdDDDDDDdDDDDdddddRrdddDdddDDdddgdggggppgppppppppppppppppppggppppppppppppppppppppppppppppppggppppppgggdddddDDDddddxSxrSrrSxxdddddddDDDDDDDddddqqllllqddqlllllllllllllllllllllqqddddddqlqdddDDDD^^!!!^^DDDddddddddddppmmmmmmpppppmmmmpyyyyyyyyqqqqsss~s~~~~~~~~~~~~~~~~~~sqpppppppppp^^!!^^^^^pppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqdq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppppppppi^^^^i^^p^pppq~~~~~~
~~~~~~~~~~~~~~~~~~~~~ssqgdggggggggggq~~~~~~~~~~~~~~~~ssqqdddddddddddqq~~~~~~~~~~qdddddDdDddddddddDDDdpddpppppp^^^xx^^^^^^^^^^^^^^!^^^^^^^^^^^^^!!^^^pppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqdddDDDDDDDDDDDDDDDdDDDddddrRdddDddddDddddddggggpgggppppppppppppppggggpppppppppppppppppppppppppppppggggppppppgggggddddDDdddddxxrrSSSxddddddddDDdDDDDDdddddqllllqddqqllllllllllllllllllqdddddddqlllqdddddDD^!!!!^DDdDDDdddddddppmmmmmmmpppmmmmmmpyyyyyyyyyyyqsss~~~~~~~~~~~~~~~~~~~~qpppqpppppp^^^^^^^ppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqpprrppppii^iiii^^^pppqs~~~~~
~~~~~~~~~~~~~~~~~~~~~~sqgggggggggggq~~~~~~~~~~~~~~~~~sqdddddDDDDDDddddq~~~~~~~~sqddddddDdddddpdddddDddpppppppp^^^xxxxx^^^xxx^^^^^^^^^^^^^^^^^^!!!^^^^pppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddDDDDDDDDDDDDDDdDdDDddddrRdddddddddddgggggggggpggpppppppppppppggggpppppppppppppppppppppppppppppggggpppppppgggggddddDDdddddddrSxSxdddddddddDDdDDDDDDdddqllllqdddddqllllllllllllqllllqdddDDddqqlllqddddDD^^!!!^^dDDDDDdddddpdpppmmmmmmmmmmmmmmpyyyyyyyyyyyyqsss~~~~~~~~~~~~~~~~~~~~qqqsqqqpppp^^^ppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssrrpprrppppippirr^^ppqs~~~~~~
~~~~~~~~~~~~~~~~~~~~~~qgggggpggggqqs~~~~~~~~~~~~~~~~ssqddDddDDDDdDdddddq~~~~~~~sqdddddddddpdpppdddddddpppppxp^^^^^xxxxxxxxxxx^^^^^^^^^^^^^^^^^!^^!^^^^ppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddDDDDDDdddDDDDDddDddddrRdddddddddddgggggggggppggpgpppgggpppgggggppppppggppppppggggppppppppppggggggpppppppggggdgdddddddddddrxSSxxxddDDDDdDDDDDDDDDDDdddqllllqdddddqllllllllllqdqqqqdddDDDDdddqlllqdddDD^^^!^^DDDDDdDdddddddppppmmmmmmmmmmmmmpyyyyyyyyyyyyyqqqqs~~~~~~~~~~~~~~~~~~sssssqppppppp^ppppppppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~sqppppprrrppprri^^^ppqs~~~~~~
~~~~~~~~~~~~~~~~~~~~~~qpgggppgggqss~~~~~~~~~~~~~~~~ssqdddDDDDDDDDDDDdddqs~~~~~~qddddpddddddpppppppdddppppppp^^^xxxx^^xx^^xxxxx^^^^^^iiiiiii^^^!!!!!^^^ppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddDDDDddddddDDdddddddRrdddddddgddggggggggggggggggggggggggggggggppppgggppppppppgggggpppppppgggggggppppppppggggggddddddddddrdxxxddddDDDDdDDdDDDDDDDDddddqllllqqqdqllllllllllqddddddddDDDDDddddqllqdddDDD^^^^^DDD^DDDdpdpdddddppmmmmmmmmmmmmmmpppppyyyyyyyyyyyyqs~~~~~~~~~~~~~~~~~~~~ssqppppppppppqqqqqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqss~~~sqpppppppprrrpi^!^^pqs~~~~~~~
~~~~~~~~~~~~~~~~~~~~~sqppgppppggqs~~~~~~~~~~~~~~~~~sqddddDDDDDDDDdDddddqs~~~~~sqddppddddddpppppppppddpppxpxx^^xxxx^^^^^^^^xxxx^^^^^iiiiiiiiii^^^^!!!^^^ppppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qddddddddddgddddddddddddrRdddddddgggdggggggggggggggggggggggggggggggpppgggggpppppppggggggpppggppggggggpppppppppggggddddddggddrdddddddddDDDdDDDDDDDDDDDDDdddqllllllqdqllllllllllqdqdddddDDDdDDdddddqlqdddDDDDD^^DDD^^DDDddddpdddppppmmmmmmmmmmmmmmmmmppyyyyyyyyyyyqqs~~~~~~~~~~~~~~~~~~~sqppppppppppqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddqs~ssqppppppppprppii^!^^pq~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~sqpppqqqqqs~~~~~~~~~~~~~~~~~~sqddddpDDDDdDdddddddqs~~~~~sqdppppdddddpppppppppppppxxxpxxxx^^^^^^^^^^^^xxxxppiiiiiippppiiii^^^^!^^^ppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddddggdgddddddddrRddddddggggggggggggggggggggggggggggggggggggpgggggggppppppppgggggggggggggggggggppppppppgggggdggddgggrggdddddddDDDDDDDdddddddDDddddqllllllllqlllllllqqlllqlqdddDdDdddDDddddqllqdDDDDDDD^^DD^^^Dddddddpdppppppmmmmmmmmmmmmmmmmppyyyyyyyyyyyyyq~~~~~~~~~~~~~~~~~~~~qpppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qddddqssqpppppppprrppp^i^^^ppqs~~~~~~~
~~~~~~~~~~~~~~~~~~~~~sqppppqssss~~~~~~~~~~~~~~~~~~~~sqddddddDDdddDddddqs~~~~~~sqdppppppddppppppppppppppxxxxxx^^^^^^^^^^!^^^xxxppxppiippppppppiiii^^!^^^ppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qdddddddddgg^^ddd^^ddrRddddddggggggggggggggggggggggggggggggggggggpgggggggggppppppggggggggggggggggggggppppppgggggggggggggrggddddddddDDDdddddddddddDdddddqllqqqllllllllllqddqllllqddDDDdddddDdddqllqdddDdDDD^D^d^^!^dddddddpppppppppmmmmmmmmmmmmmmmppyyyyyyyyyyyyyyqs~~~~~~~~~~~~~~~~~~~qppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqggqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qddDDdqssqppppppprppppi^^^!^ppqs~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~qqqqs~~~~~~~~~~~~~~~~~~~~~~~~~sqqdpdddDDdddpddqss~~~~~~sqpppppppppppppppppppppxxxxxxx^^^^^!!^^!!!!^^^xpxpppppppppppppppipii^!!^^^pppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqdddgdg^^^^^^^^^^drRdddddggggggggxggggggggxggggggggggggggggggggggggggggggpggpggppggggggggggggggggggpppppggggggggggrrrgggddddggddDDddddddddddddddddddrrqdddqrlllllllllqdqlllqdddDDDdddqqdddqlllqdddddd^^^DDD^!^^dddddppppppppppppmmmmmmmmmmmmmmppyyyyyyyyyyyyyyyqs~~~~~~~~~~~~~~~~~~qppppppqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqggqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qdDDDddqssqpppppprppppi^^!^^ppqs~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~sqppdddddddddqqss~~~~~~~sqxppppppppppppppppppxxpxxxx^^^^^!!!!^!!!!^^^^xxxxpxpppppppppppppppi^^^^^^pppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqdggggg^^!^!!!h^^drRrdd^^gggggggxxggggxgggggggxxxggggggggggggggggggggggggggppppppgpgggggggggggggggppppgggggggggggrgggggddddgggddDDdddddrrrrrrdddddrrdddddddrqqlllllllqdqllqddDdDDDddqlqddqlllllqdddd^^^^^D^^^^Ddddpppdppppppmpmpmmmmmmmmmmmmmmmpppyyyyyyyyyyyyyqs~~~~~~~~~~~~~~~~~~~qpppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqggggggqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdDDddqsssqqppprppppii^^!!^pqs~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpp^ddd^^ddpqs~~~~~~~~sqpppppppppppxppppxpppxxxxxx^^^^^^^^!!!!!^^^^^xxpppppppppppppppppppppp^^^^^pppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggg^hh!!!^^^drR^^^^ggg^^^xx^^xxxxgxxgxxxgxxxxggxggggggggggggggggggggppgggppppgggggggggggggggpggpggggggggggrggggggdggggdgddDdddddrddddddrrrrrddDDddddrdddqlllllllqlllqddDDDDDddqllqqlllllllqqddd^!!^DD^^DDddddpddppppppmmmmmmmmmmmmmmmmmmmppppyyyyyyyyyppqs~~~~~~~~~~~~~~~~~~~~~qqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdDdqs~~~sqppprppppiii^^!^ggq~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qpp^^^d^^^ppppq~~~~~~~~sqxppppppxppxxxpppppxxxxxxxxx^^^^^^LV!!^^^^xxxxpppqpppppppppppppppppppp^^^^pppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qggggggggg^^^^!!^^^^*^^^^^gg^^^^^^^xxxgxxxxxxxxxgxxxgxxxgxgggggggggggggggggggggpppppggggggggggggggggggggggggggggrggggggggggggdddddddddrddddddddddddDDDddddrddddqllllllllllqddDDDDdddqllllllllqqlllqdd^^!^^^DDDDDDdddddppppppmmmmmmmmmmmmmmmmmmmppppyyyyyyyppppqss~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qgggggggggqs~~~ss~~~~~~~~~~~~~~~~~~~~~~~sqddqs~~~~~sqqrpgggppi^^!!^ggq~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qp^^^^pd^ppppqs~~~~~~~~sqxxxppxpxpxxxppppppxxxxxxxxxxxhh^LVV!!^^^xxxxxxpqsqpppppppppppqqqpppppp^^ppppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqqqqggggg^^!!!^^^^^^^^^^^^^^^^^xxxxxxxxxxxxxxhhxxxxxggggggggggggggggggggggpppggpppggggggggggggggggggggggggggrggggggggggggdddddddrrddddddddddddDDDDddddrdddqllllllllllqdddDDDdddqllqlllllqddqlqdddd^!!^^DDD^ddddddppppppmmmmmmmmmmmmmmmmmmmmpppppyyyppppppppqssqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqggggggggggqs~sqqqs~~~~~~~~~~~~~~~~~~~~~~qddqs~~~~~~ssqggggggi^^^^^ggq~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqp^^^^ppppppqs~~~~~~~~sqxxpppppxxxxxxxxpxxxxxxxxxxxxxhhLL^L^^^^^xxxxpxppqsqppppppppppqsssqqqppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqggggg^^^^^^^^!!^^^^!!^^^xxxxxxxxxxxxxxhxxhxxxxxgxggggggggggggggggggpppppgggggggggggggggggggggggggggggggrggggggggggggddddddrddddDDDDDddddDDDdDdddrdddddqqqllllllqdDdDDddddqllqdqllllqddqllqddd^!!!^^D^^dddddpdpdpppppmmmmmmmmmmmmmmmmmmpmmmpyyppppmpppppqqppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggggggqssqdddqs~~~~~~~~~~~~~~~~~~~~~~qqs~~~~~~~~sqgggggiggg^^gggq~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpp^pppppqqs~~~~~~~~sqxxpxxxxpxxxxxxxxpxxxxxxxxxxxxxLLh^^!^^^xxxxxxpxxpqssqpppppppqqs~~~ssqpppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggg^^^^^!!!!^^!^^^^xxxxxxxxxxxxxxhhxxxxxxxxxxxggggggggggggggggggggpppggggggggggggggggggggggggggggggrgggggggggggggdrrrrddDDDDDDDDddDDDdddddrrddDddddddqllllqddDDDDdddqllllqllllllqddqllqd^^!^^!^^^DDdddddddddppppmmmmmmpmmmmmmmmmmmmmmppppppppmmpppppqpppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qgggggggggggqssqddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggggg^gggqs~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqppppqqqss~~~~~~~~sqxxxxxxxxxxxxxxxxxxxxxxxxxxxxxLLhh^!!^^^xxxxxxpxxppqsqpppppqqqs~~~~~~ssqqqqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqggggggg^^!!!!!^^^xxxxxxxxxxxxxxhhhxxxxxxxxxxgggggggggggggggggggggpppgggggggggggggggggggggggggggggggrgghgggggggggrpdddddDDDDDDDDDDDDdddddrddddDDdddddqqlllqdddDDDddqllqqlllllllllqqdqlqdd^^^^!!^^d^ddddddddddppppmpmpmppmmmmmmmmmmmmmmppppppmmmmpppppppppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqggggggggqqs~sqddddqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggg^ggggqs~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpqqpqs~~~~~~~~~~~sqxxxxxxxxxxxxxxxxxxxxxxxxxxxLLxx^^^^^^^xxxxxxxxxxqqssqpppppqss~~~~~~~~~sssssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqgggggggg^^!!!!^^xxxxxxxxxxxxxxxxhxxxxxxxxxxxxxgggggggggggggggggggppggggggggggggggggggggggggggggggggrghhgggggggggrppdddddddDdDDDdDDddddrrdddDDDDDDdddddqlllqddDDDdqllqddqllllllllllqllqddD^D^!!!^^^dpdddddddddppmmpppmmmmmmmmmmmmmmmmmmpmmpmmpmmmmmppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqggggggxxqss~sqddDdqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qgggggggg^^ggggq~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqssq~~~~~~~~~~~~sqxxxxxxxxxxxxxxxxxxxxxxxxxxxLxxxx^^!!^^xxxxxxxxqqqss~~sqpppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggx^^^^!^^xxxxxxxxxxxxx^^xxxxxxxxxxxxxxggggggggggggggggggggpgggggggggggggggggggggggggggggggggrghhhgggggggrppdpdddpddDddddDDDdddrdddddDDDDDDDDdddqlllqddDDDddqlqdqlllllllllllllqdddDDD^!!!!^^dddddddddppppmmppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggxxx^^qs~sqdddDddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qggggggg^^^^ggqs~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxxxxxxxxxxxxxxxxxLxxxx^^!!^^xxxxxxxxqsss~~~~~sqqqs~~~~~~sqqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqqggggx^^^^^^^^xx^^xxxxx^^^^^xxxxxxxxxxxxgxgxggggggggggggggggggggggggggggggggggggggggggggggggggggrggggggggggrrpppdpppppddddddDDDddrdddDDDDDddddddddqlllllqddDdddqllqllllllllllllllqddDDDD^!!!!^ddddddpddpppppmpppmpmmmmmmmmmmmmmmmmmmmmmmmmmmmppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qgxxxxx^^ssssqddDDdDddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqggggggg^^^ggqs~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqxxxxxxxxxxxxxxxxxxxxxxxxxxxLxxxxx^^!^^xxxxxxxxqs~~~~~~~~~~sss~~~~~sqddqqqqssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqqxxxx^^x^^^^x^^^^^xx^^^^^^^xxxxxxxxxxxxxgggggxggggggggggggggggggggggggggggggggggggggggggggggggrrrrggggrrrgppppppppppdpdddddddddrdddDDDDddgddddddqllllllqdddddqlllllllllllqqlllqqddD^D^^!!^^^dddppppdppppppppppmpppmmmmppmmmmmmmmmmmmmmmmmmmmmmppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qxxxxx^^^^sssqddDdDDddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqgggggg^ggqs~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqxxxxxxxxxxxxxxxxxxxxxxxxxxxxxLxxxx^^^^^xxxxxxxxxqs~~~~~~~~~~~~~~~~~sqdddddddqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqxxxxxxxxxxx^^^^^^^^!!^^^^xxxxxxxxxxxxgxxxxggxgggggggggggggggggggggggggggg^ggggggggggggggggggrgggrrrrggggppppppgpppppdddddddpprddddddddgggddddgqqlqqlllqdddqlllllllllllqddqlqdddd^^^^!!^^^dpdppppppppppppppppmpppmpmmppppppmmmmmmmmmmmmmmmmmmppppppqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxx^^LL^sssqddDDDDdqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqggggggqs~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxLxxx^^!!^^xxxxxxxxqs~~~~~~~~~~~~~~~~~~sqdddDDDdddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxx^^^^^x^^^^^^^^!^^^xxxxxxxxxxxxxxxxxxxxxgggggggggggxxggggggggggggggg^^^^qgqggggggggggrrrggggggggggggppggggpppppppddddpdpprpddpddddggggdgggggqggqqllqdqlllllllllllqddqllqdddd^^!!!^^ddpdpppppppppppppppppppppppmmpppppmmmmmmmmmmmmmmpmmmmmpmmppppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxx^^VL^^sqddDDDDDddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqggggq~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxLxxx^^^!^^^xxxxxxxqs~~~~~~~~~~~~~~~~~~sqqddDDDDDdddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqxxxx^^^^^^^^^^!^^!!^^^xxxxxxxxxxxxxxxxxxxxxxxggxgggggggxggxggggggggggggg^^^^lqlqggggrrrrrggggghhggggggggggggppppdddpppdpppppprpppddddpgggggggggggggggqllqlllllllllllqdddqlqddddd^^!!^^ddddpppddpppppppppppppppppppmppppmmmmmmmmmmmmmmmmpmmmppmmmpppppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxqs^V^^^^qdddDDDDDdq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqgqqs~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxxxxxxxxxxxxxxxxxxxLxxxxx^^!^xxxxxxxxxxqs~~~~~~~~~~~~~~~~sqdddDDDDdDDDdddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqxxxxx^^^^^^^^!^!^!!!^^xxxxxxxxxxxxxxxxxxxxxxxxxgggggggxxxxgxxggxggggggg^^^!^^llllqqgrgggggggggghhhghhhgggggpppppddddddpppppprrpppppdppppggggggggggggggqlllllllllllllqpppdqllqdddd^^^^ddddddppdddpddpddpppppppppppppppppppmmmmmmmmmmmmpmppppmpmmmmpppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqs^^^^ssssqddDdddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qgqs~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxxxxxxxxxxxxxxxxxxxLxxxxxx^^^^xxxxxxxxxxqs~~~~~~~~~~~~~~~~sqddDDdddddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqxxxxxx^^^!^^^!!^!!!^^^xxxxxxxxxxxxxxxxxxxxxxxxgxxxgxgxxgxxxxxgggxggggg^^!!!!^^^lllllrggggggghgghhhhghhgggggppppppdddddpppdpprppppdpdppppgggppggggppgggggqqllllllllllllqppqllqppdddd^^ddddddppdddddpdddddppppppppppppppppppmmmmmmmmmmmmmmpppppppmmppppppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss^^ssssqddddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~q~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxqqxxxxxxxxxxxxxxxxxxxxxxLLxxxxxx^^^xxxxxxxxxxqs~~~~~~~~~~~~~~~~~sqddddddqqddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqxxxxxxx^^^^!!^!!!^!!!^^^^xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxgxxxxxxxxxxxgxggg^^!!^^^^llllllqgggggghhghhhggggggggggpppppdddddddddppprpppddddpppgggppppggppppggggggqlllqqlllllllqqlllqpdddddddddpppppppdddddddddddpppppppppppppppppppmmmmmmmmmmmmmmmpppppppppppppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqx^qsssqdddqqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxqqqssqxxxxxxxxxxxxxxxxxxxxLLxxxxxxx^^xxxxxxxqqqqs~~~~~~~~~~~~~ss~~sqddddqqqssqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqxxxxx^^^^^^^!!!!!!!!!!^!^^xxxxx^^^xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxgg^^^^^!^^^llllllll^^^^gghhghhhgggggggggpppppdddddddddpppprpppddddpppgggppppgppppppggggggqlqddqllllllllllllqddddddddpppddppddddddddddddpddpppppppppmmppmmmmmmmmmmmmmmmmmmppppppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqxxqs~sqddqs~sss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxqssssqxxxxxxxxxxxxxxxxLLLLLxxLxxxxxxxxxxxxxqqssss~~~~~~~~~~ssssqqs~~sqqqqss~~~ssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxx^^^^^^^^!!!!^!!!!^!^^^xxx^^^^^xxxxxx^^xxxxxxxxxxxxxxxxxx^^xxxxxxxx^^^ll^^^lllllllll^^^^^gggggggggggggghgppppppppddpdddddpppprpppppdpppgggpppppppppppgggggqllqddpqllllllllllllqppdhhhppdppdddddddddddDddpddddpppppppmmmmmmmmmmmmmmmmmmmmmmmpppppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqgggqss~~sqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqssqqqxxxxxxxxxxxxxxLLLxxxxxxxLxxxxxxxxxxqqqs~~~~~~~~sss~~~ssssqddqs~~ssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxx^^^^^^^^!!!^!^!!!!!^^^^^x^^^^^^^xx^^^^^xxxxxxxxxxxxxxxx^^^xxxxxxx^^^^^ll^^lllllllll^^!!^ggggggggggggggggppgggpppppdpdddpppppprpppppppggpgppppppppppppgggqllqdqqppqlllllllllllRrphhhpppdddddpddpddDDDDdddddddpdpppppmmmmmmmmmmmmmmmmmmpmmmmpppppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqggggqs~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqxxxxxxxxxxxxxxxxLxxxxxxxxxxxLxxxxxxxxqsss~~~~~~~~sqqqssssqqqdDddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~~~~sssssqxxxxxx^^^!^^!!!!!!!^^!^!!!^^^^^xx^^^^^^^^^^^^xxxxxxxxxxxxxxxxx^^^xxx^x^x^^^lllllllllllllll^^!!^^gggggggggggggggggggpgggppppppdppppppprrppppppppppppppppppppppgggqllqllqqllllllllllqqRRpphhppddddddpdddddDDdDDdddddpdpppppppmppmmmmmmmmmmmmmmpmmmppppppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqxxxxxxxxxxxxxxxxLxxxxxxxxxxxLxxxxxxxxxqsqs~~~~~~~sqdddqssqddddDDddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqsssssqqqqqxxxxxxx^^!!!!^!^!!^^!!^^!!!!!^^^xxx^^^^^^^^xxxxxxxxxxxxxxxxxx^^^^^xx^^^^^^^llllllllllll^ll^^^!^^^^ggggggggggggggggggggggpppppppppppppppprppppppppppppppggpppgpggggqllllllllllllllqqggrRrphhpdddddddpdpddDdDdDDDddddddpdpppppppmmmmmmmmmmmmmmmmmmmmmpppppppppqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qddggddgqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxxxxxxxxLxxxxxxxxxxxLxxxxxxxxqsqxqs~~~~ssqqddddqssqddDDDddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxqqqqqxxxxxxxxxxxx^!!^^^!!^!!^!!!!!!!!^!!^^^^xxxxx^^^^^xxxxxxxxx^^xxx^^^^!!^^^xx^^^^^^^llllllllll^^^^^^!!^^^^gxgggggggggggggggggggpppppppppppppppppprppppppppppppppggpgggggggqllqlqqqqqlllqqggggrRRpphpddddddpppddDDDDDDDdddddddpddppppppmmmmmmmmmmmmmmmmmmmmmmppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qddgddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxxxxxxxLxxxxxxxxxxxxxLxxxxxxxxqxxxqs~ssqqddddddqs~sqddDddqs~~~~ssssq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxxxxxxxx^^!!^!!!!!!!!!!!!!!!!^!!!^^^^^^xxxxxxxxxxxxxxxx^^^^^^^^!!!!^^xx^^!^^^^^*^lll^^^^^^^^^!!!^^^^xxgxgggggggggggggggpppppppppppppppppppprppppppppppppppgggggggggggqqgqgggggqlqgggggggrRpppdddddpppppddDDDDDDDddddddddddppppppmmmmmmmpmmmmmmmmmmmmmmmppppppppqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qxxxxxxxxxxxxxLLLLxxxxxxxxxxxxxxxLxxxxxxxxxxxq~~~qdddddddqs~~~sqddqqs~~~~sqqqqdq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqxxxxxxxxxxxxxxxxxx^^!^!!!!!!!!!!^^!!!^^^^^!^^^^^^^^^^^xxxxxxxxx^^^^^^^^^^!!!!!^^^^^!!^^^^^^^^^^^^^!!^^!!^^^^xxgxxggxggggggggggggppppppppggpppppppppppprrppppppppppppggggggggggggggggggggqqgggggggggRrppppddpppppddddDDDDDddDDdddddddppppppmmmmmmmmpmmmmmmmmmppppppppppppppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdDDDDddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxLxxxxxxxxxxxxxxxxxxxxLLxxxxxxqxqs~~~sqqqdqqqs~~~~~sqqss~~~~sqdDdddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxxxxxxxxx^^^!!^!!!!!!!!^^^^^^^^^^^!^^!!!^^^^^^^^^^^^^^^^^^^^^^!^!^^^!^^^!^!!!!^!^^^^^^^^^!!!!!!^^^^^xxxxxxggggggggggggppppppppggggpppppppppppppprppppppppppggggggggggggggggggggggggggggggggrRpppppppddddpddddDDDDDDDDddddddppppppmmmmmmmmmppmmmmmmmpppppppppppppppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddDDDddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxLxxxxxxxxxxxxxxxxxxxxxxLxxxqqsqs~~~~~sssqsss~~~~~~~~~~~~~~~sqdDDDddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxxxxxxxxx^^^!^^!!!!!^!^^^^^^^^^^^^^^!^^!!!^^^^^^^^^^^^^^^!!^^!!^^^^^^^^^!!!!!!!^^^^^^^^^^^^^^!!^^x^^xxxxxxgggggggggggppppppppppgggggppppppppppppprpppppppppgggggggggggggggggggggggggggghgggrRppppppdddddddddddDDDDDDDDddddddpppppmmmmmmmmpppmmmmmmpppppppppppppqqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddDDDDDdqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxLxxxxxxxxxxxxxxxxxxxxxxxLLL~~~s~~~~~~~~~s~~~~~~~~~~~~~~~~~~~sqdDDdqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqxxxxxxxxxxxxxxxxxxxx^^!^^!!!!!!^^^^^^^^^^iii^^!!!!!!!!!^^!!^^^!^^^!!!!^!!^^^^^i^^^^!!!!!!!^^xx^x^^^^^^^^^^^^xxxxxxxggggggggggggggpggppppppppggggpppppppppppprpppppppgggggggggggggggggggggggggggggggggggRrdpddppddddddppddDDDDDDDDdddddddddpppmmmmpmmpppmmmmmmphhhpppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qdddddDdddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxqqqxxLLxxxxxxxxxxxxxxxxxxxxxxxxqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxxxxxxxx^^^^^^!!!!!^!^^^^^^^^iiiiii^^^!!!!!!^!^!!!!!!!!^^^!!!!^^^^^^^iii^^!!!!!!!^^^^^^^xx^^xxx^^^^^xxxxxxgxgggggggggggggggppggpppgppppgppppppppppppprppppggggggggggggggggggggggggggggggggghgggRrddddddpdddddddddDDDDDDDDddddddddddpmmmmppppdpdpmmmmphhhhppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqdDDdqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxqsssqLLxxxxxxxxxxxxxxxxxxxxxxxxxxqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqxxxxxxxxxxxxxxxxx^^^^^^^^!^!^^^^^^^^^^i^^iii^^^^!!!!!!!!!!!!!!!!!^!^^!!^^^^^^^iiii^^^^^^!^^!!^^^^xxxxxxxxxx^^xxxxxxggggggggggggggggggggggggggpggppppppppppppppprpppppgggggpgggggggggggggggggggggggggghhggRRddddddddddDDddDDDDDdDDdDddDDddddpddddpmpddddddppmmpphhhpppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qxxxxxxxqsssssqxxxxxxxxxxxxxxxxxxxxxxxxxxxqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxxxxxxxx^^^^^^^^^!^^^^^^^^^^^ii^^^ii^^^^^^!!^^^^^^!!!!!!!!!!!!!^^^iiiiiiiiiiii^^^!!!^!!!^^xxxxxxxxxxxxxxxgxxxgggggggggggggggggggggggggggggppppppppppppprpppppppgpppppggggggggggggggggggggggghhhgprRddddddddddDDDDDDDDDDDdDDDDDdDDDddddddmdddddddpddmmphhhppppqqpqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qxxxxqqxqsssqqqxxxxxxxxxxxxxxxxxxxxxxxxxxxxqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxxxxxx^^^^^^^!^!!!!^^^^^^^^iii^^^^ii^^^^^^!^^^^^^^^^^^^^^!!!^!!^^^^iiiiiiiiiiii^^^!^^^^^^^^^xxxxxxxxxxxxxxgxgggggggggggggggggggggggggggggggpppppppppppprppppppppppppgggggggggggggggggggggggghhhhprRddddDDdDDDDDDDDDDdDDDdDDDDDDDDDddddddddddddDdddpddphhppppqssqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qxxqqssqsssqxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqxxxxxxxxxxxxxx^^^^^^!!!!!^^^^^^iiiii^^^^!^^iiii^^^^^^^^^^^^^^^^^^!!!!!!!^^iiiiiiiixxiiii^^^^^xxxxxxxxxxxxxxxxxxxxxxxggggggggggggggggggggggggggggggggpppppppppppprpppppppppppppggggggggggggggggggggggghhhprRrddddDDDDDDDDDDDdddDDDDDDDDDDDDddddddddddddDdddddddppppqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqss~~ss~sqxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqxxxxxxxxxxxxx^^^!!!!!!!!!^^^^^iiiii^^!!^^^^^ii^^^^^^xxx^^^xx^^^^^^!!^!^^^ixiiiixxxxxiii^^^^xxxxxxxxxxxxxxxxxxxxxgxxggggggggggggggggggggggggggggggggpppppppppppprppppppppgppgggggggggggggggggggggpggghpprRRrdddddDDDDDDDDdddddDDdDDDDDDDDDDDDDdDDddDDddddddpppppqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~sqxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqxxxxxxxxxxxx^^!^!!!!^!!!^^^^^^iiii^!!!^^^^^iixxxxxxxxxxxxxxx^^^^!!^^^^^ixxxiixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxgggggggggggggggggggggggggpggggggggpppppppppppprppppppggggpgggggggggggggggggggpppggppppprRRrddddDDDDDddddddddDDDDdDDDDDDDDDDDDDDDDDDDDDddddpppqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqxxxxxxxxxxx^^^!!!!!!!^^!!!^^^^^^i^^!!!^^^iiixxxxxxxxxxxxxxxxxx^^^^^^^^xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxgxgggggggggggggggpggggggggppppggggggpppppppppppprpppppgggggggggggggggppggggggpppppppppppprRRrddddDDdddddddddddDdDdddDDDDDDDDDDDDDDDDDDdddddddpqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqxxxxxxqqxxxxxxxxxxxxxxxxxxxxxqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqxxxxxxxxxxx^^^!!^!^!^^!!!!^^^^^i^^^^!^^xxxxixxxxxxxxxxxxxxxxxxxxx^^xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxgggggggggggggggpggggggggppppppppggggpppppppppppppppgggggggggggggggppggggggggppppppppppppprRrddddDdddddddddddddDddddDDddddDDDDDDDDDDDDDdddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqxxxxqssqxxxxxxqqxxxxxxxxxxxxqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxx^^^!!!!!!^!!!!!^^^iiiixxx^^^xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxgxgggggggggggggggpppgggggggppppppppppppppppppppppppppgggggggggggggggpgggggggggppppppppcppppprRrddddddddydddddddddddddddddddddDdDDDDDDDDDddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxqsssqxxxxqqsqxxxxxxxxxxxxxqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxx^^^!^!!!!!^!!!^^^iiiixxxxx^xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxgggggggggggggggpppggggggggggppppppppppppcppppppppppggggggggggggggpppgggggpggpppppccccccppppprRRrddddyyyyydddddddddddddddddddddDDDDDDDdDDdddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqs~~~sqqqqssssqxxxxxxxxxxxxxxq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqxxxxxxxx^^^^^^^!!!^^^^!^^^^iixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxgggggggggggggpppppgggggpgggpppppppppppppcccppppppppgppgppggggggggpppgggggppgpppppppcccccccppppprRrdddyyyyyyddyydddddddyyddddddddDdDDDddDdddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~ssqxxxxxxxxxxxxxxqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqxxxxxx^^^^^^^!!!!^^^^^^^iiixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxgxxgggggggggggggpppppggpppggpppppcpppppppccccccpppppppppppggggggggggppppgggpppppppcpccccccccccppppRrddyyyyyyyyyyyyyydddyyyyyydddddDDdDddddddddddddqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqxxxxxxxxxxxxxqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxx^^^^^!!!!^^^^^^^^iixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxggggggggggggggppppppppgggppppcccgppppccccccpppppppppggggggggggggppppcgppppppppppcccccccccpppppprRryyyyyyyyyyyyyyyyyyyyyyyyyddddddddddddddqqqqqddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxqxxxxxxqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxx^^^^!!^^!!^^^ii^^iixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxggggggggggpgppppgpppppppgppppcpccpcppcccccpcpccppppgggggggggggggppppcpppppppccpppccpcpccppppppppRryyyrRRRyrrrrrryyyyyyyyyyyydydddddddddddqssssqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqdddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqqsqqxxxxq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~ss~~~~~ssssqxxxxxxxx^^^^!!!^!!^^^^iiiiiiixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxgxgxggggggggggpppppgggpppppppgpcccccccccccccccccccpppgggppggggggggppppppppppppcccpppccppppppppppppprRRrrRrrRRRRRRRRRRRrrryyyyyyyyyyddddddqqqss~~~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssssssqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqqqssssssqqsqqxxxxxx^^^^!!^!^!^^^^^i^^iiixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxgxxggggggggggppggggggppgggpggpcccccccccccCcCCccpcppppgpppppcgggggppccppcppcpppcppccpcppccpppppppyyrRrRRRyyyyyyyyyyrrRRRRRRryyyyyyqdqqdddqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssssssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxqqqqqqxxqxxxxxxx^^^^^!!!!^!^^^iii^^iiixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxgggggggggggggggppggggpcgcccCCccCccCCCCCCcccccppppppppccgggggpcccccccpppppppcccpppcccpcpcpyyyyyRryyyyyyyyyyyyyyyyyyyrrRryyyyyqqssqdddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqsss~~~~~ssqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssqqxxxxxxxxxxxxxxxxxxxxxx^^^^^!!^!!^^^ii^^^^iiixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxggxgxxggggggggggppggggcccccCCCCCCCCCCCCCccccccpppppppccccggggcccccpcpcpcpppcccccpcccpccccyyyyyyRryyyyyyyyyyyyyyyyyyyyyrRryyyqss~ssqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqxqqss~~~sqqxxqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqqxxxxxxxxxxxxxxxxxxxxxxxxx^^^!!^^^^^^^i^^^!^iixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx^xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxggxxxxggggggggggpgggcccccCCCCCCCCCCCCCCCccccppppppppcccccpggcccccccccccpccccccccccccccccccycyyRryyyyyyyyyyydddddyydyyyrRryqss~~~~sss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxqs~~sqxxxxxq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxxxxxxxxxxxxxxxxx^^^^!!!!^^!!^^^^!^^ixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx^^^^^xxxxxxxxxxxxxxxxxxxx^^^^^^xxxxx^xxxxxxxxxxxxxxxgxxxxggggggggggggggccccCCCCCCcCcCCCCCCcCCcccccpppcpcpccpcccpcccccccccccppccccccccccccccccccyyrRrddydydyyyyddddddddydyyyrRR~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxqs~ssqxxxxq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qxxxxxxxxxxxxxxxxxxxxxxxxx^^^^^^!^!!!!!!^^^^^^^xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx^^^^^xxxxxxxxxxxxxxxxxx^^^^^^^^^^xx^^^^^xxxxxxxxxxxxxxxxxggggggggggggggcccCCCCCCCCcCCcCCCccccccccppppccccccCcccccccccccccccccpcccccccccCCCccccccyyRrddddddyyyyyyyddddddyyyyyyyqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxqs~sqxxqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxxxxxxxxxxxxx^^^^^!!!!!^!!^^^^ii^^^xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx^^^xxxxxxxxxxxxxxxxxxxx^^^^^!!^^^^^^^^^xxxxxxxxxxxxxxxxxxggggggggggggggcccccCCCCccccCCCcccccccccpppppccccccCCCcccccccccccCcccccccccCccCCCCCCccccyyRrddddddddyyddddddddddyyyyyyyyqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxqs~~~sqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqxxxxxxxxxxxxxxxxxxxxxxx^^^!^!!!^^^^!!^^^iiiixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx^xx^^xxxxxxxxxxxxxx^^^^!!!!!^^^^^^^^!^^xxxxxxxxxxxxxxxxxxggggggggggggggggccCCcccccgccccccccgppppgppcpcccccCCCcccccccccCCCccccccCCCCcCCCCCCCccccyrRyydddddddddddddddddyyyyyyyyyyyqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqxxxxxxxxxxxxxxxx^^^xx^^^^^^!!!!^^^^^^^^^^iixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx^^^xxxxxxxxxxxxx^^^!^!!^!!^^^^!^^!!!^^xxxxxxxxxxxxxxxxxgggggggggpggggggpccccccgggcccccccgggpppgppcccccCCCCCCCccccCccCCCccccccCCCCCcCCCccccccyyRryyyyddddddddddddDdddyydyydyyyyqsq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qxxxxxxxxxxxxxxx^^^^^^^^^^^^^^!!!^^^^^^^^^^iixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx^^^^^xxxxxxxxxx^^^^!^^^^^^^!^V^^!!!^^!!^^^xxxxxxxxxxxxxxxgggggppppppggggppccccpccgcggcgggcgggpgggpcccccCCCCCCcccccCcCccCCccccCCCCCCCccccccccyyyyRryyyddddddDddDddDDddddddddyyyyyyqyq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddppqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqxxxxxxxxxxxx^^^^^^^^^^^^^^!!^^^^i^^^iixiixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx^^^^^!!^xxxxxxxxx^^^!!!!^^^^V^^^^L^^^^^^^^^^^^^xxxxxxxxxxxxxxxggggpppppppppgpcpccpppcccggggggggggggggccccccCCCCCcCCcccCCCCccCcccCCCCCCcccccccccyyyyRryydddddDDDDddDdDDddddddddddyyyyyyyq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddppqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxx^^^^^^^^^^^^!!!!!^^^ii^iiixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx^^^^^^^!^^^^xxxxxx^^^^^^!^^h^L^^^^^Lh^^^^^^^^^xxxxxxxxxxxxxxxgxggggppppppppppppcpccppppccggggggggggggggggcccccCCcCCCcCccCCCcCccCCCCCCCcccccccccyyyyyyRryyyddddddDDddDDDdDddDddddyyyydyyyqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqddddppppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxx^^^^!^^^!^^^!^!!!^^^^^iiiixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx^^^!!!!!!^^xxxxxxxxxxx^^^hhhL^^^!^^hLhh^^^^xxxxxxxxxxxxxxxxxxxxggggppppppppppppppgggggppggggggggggccggggggcccCCcCCCCCCCCCCCCCCCCCCCccCccccccccyyyyyyrRyyyddddDDDDDdDdDDdDDDDDDdddydddyyyyqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqddddpppppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxx^^^^!!^^^!!!!!!!!^^^^^^^iiixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx^^!!^^^^^xxxxxxxxxxxxx^hLLhh^!!^hhhLxxxxxxxxxxxxxxxxxxxxxxxxggggggpppppppppppppppgggpggggggggggcccggggggcccCcccCCCCCCCCCCCCCCCCCccccccccccccyyyyyyrRryydddDdDDDDDDDDDDDDDDDDdddyddddyyqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddpppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxx^^^^!^!^^^!!!!!!!^!!!^^^iiixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx^^!^^x^^xxxxxxxxxxxxxxLLxh^^!!^^^xxLxxxxxxxxxxxxxxxxxxxxxxxxgggggpppppppppppppppppgggggggggggcccccgccccccccCCCCCCCCCCCCCCCCCCCcccccccccccyyyyyyyrrrRrdddDDDDDDDDDDDDDDdDDDddddyydddyyyqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxx^^^^!!!^!!!!!^!!!^!!^^^iixixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx^^^xxx^xxxxxxxxxxxxLLLxx^^^^^^^xxxLxxxxxxxxxxxxxxxxxxxxxxxxxggggggpppppppppppppgggggggggccccccccccccccccCcCCCCCCCCCCCCCCCCCCccccccccyycyyyyyyyrryrrRrdddDdDDDDDDDDDDDDDDDddddyyydyyyyqss~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqqddppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxx^^^^!!!!!^!!!!!^!!^^^^iixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx^xxxxxxxxxxxxxxxxxxLxxxxxxx^^^xxxxxLxxxxxxxxxxxxxxxxxxxxgxxxgggggppppppppppppggggggggpggcccccccccccccCccCCCCCCCCCC^^CCCCCCCcccccccyyyyyyyyyyyrryyyyrRdddddDDDDDDDDDDDDDDdddyydyyyyyyqss~~~~~~~~~~~~~~~~~~~~~~sqs~~~~~~~s~sss~~~~~~~~~~~~~~~~~~~~~s~~~ssssssqqppppppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qxxxxxxxxxx^^^^!!!!!!!!^!!!^!^^^iiiixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxLLxLLLLxxxxxxxxxxxxxxxxLxxxxxxxxxxxxxxxxxggxggggggggppppgggppppppppgggppppccccccccccccccCCcCCCCCCCC^^^^^CCCcccccccccccyyyyyyyrrryyyyyydRrdddDDDDDDDdDDDDDdDDdyydddyyyyyqssss~~~~~~~~~~~~~~~~~~~sqdqs~~~~ssss^^^s~~sss~~~~~~~~~~~~~~sqssssqsqssssqqqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqxxxxxxxxxxxx^^!!!!!^!!!^!!^!^^^iiiixxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxLLLLLLLLLxxxxxxxxxxxxxxxLxxxxxxxxxxxxxxxxxxgxxggggggggpgggggggpppppggggpppcccccccccccccCCCCCcCCCCCC^^^^^^CCCc^^ccccccccyyyrrrrryyyyydyddRrddDDDDDDDDDDDDDDDDDdddyydyyyddyqsqqs~~~~~~~~~~~~~~~~~sqdddqssqqsqq^^^^^sss^^ss~~~~~~~~~~~sqpqqqqpqpqsssssssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxxxx^^^!^^!^!!!!!^!^^^^iiiiixxxxxxxxxxxxxxxxxxxxx^^xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxLLxxxxLLLLLLLLLxxxxxxxxxxxxxxLxxxxxxxxxxxxxxxxxxxggggggggggggggggpppppppgggpcccpcccccccccccccccCCcCCCCCC^^!^^CCCc^^ccccccccyyyrryyyyyyyyyydddRrddddDDDdDddDDDDDDdDdddddddyydddqqyyqs~ss~~~~~~~~~~~~~sqddddqqdpqdp^^!ssss^^^^^ss~~~~~~~~~sqpgpppppppqqqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqxxxxxxxxxxxx^^^!^!!^^!!!!!^^^^iiiiiiixxxxxxxxxxxxxxxxxxxx^^^xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxLLLLLxxLLLLLLLLLLLLxxxxxxxxxxxxLxxxxxxxxxxxxxxxxxxxxxxgggggggggggpppppppggggppccccpccccccccccCccCCCCCCCCCC^!!^^^Cc^^^^ccccccyyyyryyyyyyyyydddddRrddddDdDDDDDDDDDDDddddddddddddydyyyyyqsqqs~~~~~~~~~~~~ssqdddddddd^^d^^^ss^^^!!^^^s~~~~~~~sqgggpppphppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqDDDDDDq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxx^^^^^!!!^!!!!^!!^^^iiiiiiixxxxxxxxxxxxxxxx^^^^^^^^xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxLxLLLLLLLLLLLLLLLLLLLLLxxxxxxxxxxxLxxxxxxxxxxxxxxxxxxxxxxxgxgggggggpppppppgggggcccccccccccCcCcCcCCCCCCCCCCCC^^^!!^^c^!!!^ccccccyyyrryyyyyyyyydddddRRddddDDDdDDDDDDDDDDDDdddddddyyddyyyyyqqyyqs~~~~~~~~~~~sssqdDDdd^^^^^^!^^ss^!!!!^^^s~~~~~sqqggghhhppppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqDDDDqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqxxxxxxxxxxx^^^^!!!!!^^^!!^!!^iii^^iiixxxxxxxxxxxxxxx^^!!^!!^xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxLLLLLLLLLLLLLLLLLLLLLLLLxxxxxxxxxxLxxxxxxxxxxxxxxxxxxxxxxxxxgggggppppppppppggggccpccccccccCCCCCcCCCCCCCCCCCC^^!!!^^cc^^^^cccccyyyrryyyyyyyyyddddddrRrdddddddddDDDDDDDDDddddddddyddyyyyyyqyyyqsss~~s~~~~~~~sqdDDDDdd^^^!!!^^ss^^^^!^^s~~~~~sqgggggghhhppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqDDqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qxxxxxxxxxxxx^^^^^!!!!^^^^!^!^!!^^^^^iiiixxxxxxxxxxxx^^^!!!V!^^xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxLLLLLLLLLLLLLLLLLLLLLLLLxxxxxxxxxxxLxxxxxxxxxxxxxxxxxxxxxxxgxggggggpppppppppppgpppcccccccccCCCCCcCCCCC^^CCCCC^^!!^^^^cccc^cccyyyyyryyyyyyyyyydddddddrRrqddddddDDDdDDDDDddDDDDdddddddyyyyyyyyyyqqsssqs~~~~~ssqdDDdddddd^^^^^^sssss^^^s~~~~~~sqggggggphpppppppppq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqqs~~~sqDDqs~sssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~s~~~~~~~~~sqxxxxxxxxx^^^^^^!!!!^^^^^^^^!!!^^^^^^^iiixxiixxxxxxxxx^^^^hLh^^xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxLLLLLLLLLLLLLLLLLLLLLLLxxxxxxxxxxxLxxxxxxxxxxxxxxxxxxx^xxxxxgxgggggggppppppppppppppccccccCCCCCCCCCCCC^^^CCCC^^!!!!^^^ccccccccyyyyyrqyyyyyyyyyydydddddrRsqdddddddddDDddDDDDDDDDddddddyddyyyyyyyyyqqqyqssss~~ssqdddppdddpp^^^gqqqssss~~~~~~~~sqggggggppppppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppqs~~~sqqssssqqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqsssssssqqss~~~~~~sqxxxxxx^^^^^^^!!!!^^^^^ii^^^!!^^^!^^^iiiixiiixxxxxxxxxxx^hLLxxxxxxxxxxxxxxxLLxxxxLLxxxxxxxxxxLLLLLLLLLLLLLLLLLLLLLLLLLxxxxxxxxxxLxxxxxxxxxxxxxxxxx^^^xxxxxxxggggggggpppppggpppppppccccCCCCCCCCCCCCCCCCCCC^^^!^^^^^ccccccccyyyyyqssqyyyyyyyyyyyddddqrr~sqddddddddDddddDDDDDDDddddDdddddyydyyyyyyyyyqqqqss~~ssqqqppppppggggggggqss~~~~~~~~sqgggggggppppppppqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqpppqs~~~~ss~ssqDDDDDqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqggqqqqqqqggqss~~~~ssqxxxxx^^^^^^^!!!!^^^^^iii^^^!!!^!!^^^^^iiiiiiixxxxxxxxxxxxxLxxxxxxxxxxxxxLLxxLLLLxLLLLxxxxxxLLxxxLLLLLLLLLLLLLLLLLLLLLxxxxxxxxxLxxxxxxxxxxxxxxxxxx^^xxxxxxxgxggggggggpggpgggggpcccccccccCCCcCCCCCCCCCCC^^^^^^^cccccccccccyqqqqqssssqqqyyyyyyyyyyydqs~~ssqqqqdddddddddDDDDdDDDDDdDdddyyyddddyyyyyyyyyyyqss~~~ssqpppppppggggggggqss~~~~~~sqgggggggggppqpppqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~ssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqpppqss~~~~~~~sqDDDDDDq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggggggggqqsss~~sssqxxxxx^^^^!^^!!^^^^^iiiiii^^!^!^!!^!^^^^^^iiiiixxxxxxxxxxxxxLxxxxxxxxxxxLLxxxxxxxxxxxxLLxxxxLxxxxLLLLLLLLLLLLLLLLLLLLxxxxxxxxxLxxxxxxxxxxxxx^^^^^^^^xxxxxxgggggggggggggggggggggpcccpccccCCCCCCCCC^^^CC^^^^^^^ccccccccqqqqqsssss~~~sssqyyyyyyyyqqqqss~~~~ssssqqqqqqqdddDdDddDDDDDDddddyddddddyyyyyyyyyqsss~~~~sqppppppggggggggggqs~~~~~~~sqqqqgggggqqsqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqsqqqssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqp^ppqss~~~~~~sqDDDDDDqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqggggggggggggggggqqsssssssqxxxx^^^!!^^!^^^^^iiiiiiii^!!!^!!!!^^^^i^i^iiiixxxxxxxxxxxxxLxxxxxxxxxxLxxxxxxxxxxxxxxxLxxLxxxxxxLLLLLLLLLLLLLLLLLLxxxxxxxxxxLxxxxxxhxxx^^^^!!!^^^^xxxxqqqgggggggggggggggggggppccppcccccccccCCC^^^^^^^^!^^ccccccccqqss~s~~~~~~~~~~~ssqyyyyyqqsss~~~~~~~~~~~sssssssqqdddddddDDDDDddddyyddddddyyyyyyyyqsss~~~~~sqppqpgggggggggggq~~~~~~~~~ssssqgggqss~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxqxxxqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qpppp^^ppqsssss~~~~sqqDDDDDqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqggggggggggggggggggqgqqqqqqqxxxxx^^^!!!!^^^^iiiiiiiiii^!^!^!!!!!^^^iiii^^^iiixxxxxxxxxxxxLxxxxxxxLLxxxxxxxxxxxxxxxxxLLxxxxxxxxLLLLLLLLxxxxxLLLxxxxxxxxxxxxLxxxxhhhx^^!!^^!!^^xxxxqqsssqqqqqggggggggggggppppppccccccccccCCCCC^^^^^^!!^ccccccccqss~~~~~~~~~~~~~~~~~sqyyyqss~~~~~~~~~~~~~~~~~~~~~sqdqqqqddddDDDDdddyyyyddyyyyyyyyyyyqqs~~~~~~sqqsqqpqqgggggqqs~~~~~~~~~~~~sqgqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqppp^^!^pqqqqqqqs~~~ssqDDDDDq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggggggggggggggggxxxxxxxxxx^^^^!!!!!^^^^iiiiiiiiii^^^!!^!!!!^^^^ii^^^^^^iiixxxxxxxxxxLxxxxLLLxxxxxxxxxxxxxxxxxxxxxxxxxxxxLLLLLLLLxxxxxxxLxxxxxxxxxxxxxLxxxhhhh^^^^^^^^^^xxxxqss~~~sssssqgggggggggggpggggpppppccccccccccc^^!^!!!!^ccccqqcqs~~~~~~~~~~~~~~~~~~~~sqqqs~~~~~~~~~~~~~~~~~~~~~~~~sqssssqdddddDDddydyyyyyyyyyyyyyyyyyyqs~~~~~~sssssqssqqqqqss~~~~~~~~~~~~~~sqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxxqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpp^!!!^pppDDDDDqsssssssqqqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggg^^ggggggggggggxxxxxx^^^^^^!!!^^^^^^^iiiiiiii^^^^^!!!!^!!!!^^ii^^^^^^^i^^^xxxxxxxxLxLLLxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxLLLLLLxxxxxxxxLxxxxxxxxxxxxxxLxxhhhhh^^^^xxxxxxxqqs~~~~~~sqqssqqqgggggggggggggppppcccpccc^^cc^^!!!!^!!^cccqssqs~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~ssqdddddDdddyyyyqqqyyyyyyyyyyyyyqs~~~~~~~~~~s~~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxxxxqqs~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqp^^!!^^^ppDDDDDDqqqss~ssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqggggggg^^^gggggggggxgxgxxxx^^^^^^^^!^^^^^^iiiiiiii^^^^^^!!!!!!!!^!^^^^^^!^^^^^^^^^^xxxxxxxLxxxxxxxx^^^^xx^xxxxxxxxxxxxxxxxxxxxxxLLLLxxxxxxxxxLxxxxxxx^^hhhhLLhhhhhhxxx^xxxxxqqss~~~~~ssqxxqssssqggggggggggpgpppppppcc^^^cc^^!!!!^^^^^cccqs~s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddqddddddqqqqsssqqqyyyyyyyyyyyqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxxxxxq~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqp^!!r^ppDDDDDDDDDDqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqgggg^^^^ggg^gggggxxxxxxxxx^^^^^!^^!^^^^iiiiiiii^^^^^^^!!!^^^^!!!!!^^^^!!^!!^^^^^^^xxxxxxLxxxxxxx^^^^^^^^^^^^^xxxxxxxxxxxxxxxxxxxLLxxxxxxxxxLxxxxxxx^^^^h^hhhLLhhxxxxxxxxqqqss~~~~~ssqqxgxxqs~ssqgqggggppppppppp^^ppc^!^c^^^^^!^^^cccccqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqsqddddqssss~~~~ssqqqqqyyyqqqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxxxxxxxxxq~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqp^^^^rrrDDDDDDDDDqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqgggg^^^^^^g^^^^gggxxxxx^^xx^^^^!!^^^^^^iiiiiiii^^^^^^^!!^^^^^^^^^^^^^^!!!^!!!!!!!^^^^xxxxLxxxxxx^^^^^^^^^^^^^^^xxxxxxxxxxxxxxxxxxLLxxxxxxxxxLxxxxx^^^^^^^^^hhhhLLxxxxxxxxLss~~~~~~ssqxxxgggqs~~~sqqggggpppppppp^^^^p^!!^cc^^^^^^^cccccccq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqdddqs~~~~~~~~~~sss~sqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxx^^xxxxxxqs~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqppp^^DDDrDDDDDDDqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssqqgggg^^^^^^^^!^^^xgxgx^^^^^^^^!!!^^^^^^ii^^i^^ii^^^^^^^!^^^^^^^^^^^^^^!!^!^!!!^!!!!^^^xxxLxxxxxxx^^^^^^^^^^^^^^^^^xxxxxxxxxxxxxxxxxLxxxxxxxLLxxxx^^^^^!!^^^hhhhhhLLLxxxxxL~~~~~~~~~sqxxxgggqs~~~~ssqgggqggppppppp^p^p^!!^^cccc^^^cccccccq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssssqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssss~~~~~~~~LLxxxx^^^xxxxxxqs~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqpppppDDDrDDDDDDDqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqssqqqqqgggggg^^!^^^^^!!^^^^^xx^^^^^^^!!!!^!^^^^^^^^^^^^^^^^^!!!!^^^^^^^ssssss^^^^!!!!!!^!!!^^^xxxLxxxxxxx^^^!^^^^^^^^^^^^^^^x^^^^^^xxxxxxxxLxxxxxLLxxxx^^^^^!!!!!^^^hh^^hhxxLLxxLLL~~~~~~~~sqxxxxxgxqs~~~~ssqqqqgggpppppppppp^^^^cccccc^^cccccqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssss~ssssss~sss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~~ssqqqqqqs~~~ss~qLxxx^^^^xxxxxxqs~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqppppDDDrDDDDDDDqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqgqqgggggggggg^^^!^!!^!!!!!^^^^xx^^!!^^!!^^!!!^^^^^^^^^^^^!!!^!!^^^^^sssss~sss^^^^^!!!!!!!!!^^^hhxxLxxxxx^^^^^!^^^^^^!!!^^^^^^^^^^^^^^^xxxxxxLLLLLLxxxxxx^^^!!!!!!!!^^^^^^^hxxxxLLLxqs~~~~~~~~qxxxxxxgqss~ss~sssssqgpppppppp^^pqss^ccccccccccccqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqqsqqqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqsssqqxxxxxxqs~sssqxLx^^^^^^^xxxxqss~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qppDDDDDrDDDDDDqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggggggggg^^^^^!!!!!!!!^!!^^^^x^^!!!!!^^^^!!!!^^!^!^^^^!!^!!!^^^^^ssss~~~~~s^^^^^^^^^!^^^^^^^hhhLLx^^^^^^^^!!^!!^!!!!!^^^^^^^^^^^^^^^xxxxxxLxxxxxxxxxx^^^!!^!!^!^!!^^^^^^^xxxxxxxxxqs~~~~~~~sqxxxxxqssssqqssssssqgggpppp^^^^^pqssqqqcccccqccqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddqdddppqs~~~~~~~~~~~~~sssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxqsqxxxxxxxxqssssqxxxL^^^^^^^^^xxxqs~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqDDDDDDrrDDqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqss~~~~~~~~~~~~~~~~~~sssssssqs~~ss~~ssqgggggggggggggggg^^^!!^!!^^^^^^^!^^xx^^^!^^^^^^^^^^!!!!!!^^^^^^^^^^^^^^sss~~~~~~sssss^^^^^^^^^^^^^^^hLhhh^^^^^^^^!!!!^!!!!!!!^!!^^^^^!^^^^^^xxxxLxxxxxxxxxxx^^!!!^^^^^!!!^^^^!!^^^xxxxxxqss~~~~~~~~sqqqqqs~ssqggqqs~~sqgggppp^^^!^^ppqssssqqqqqsqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqdddddddddhppqss~~~~~~~~~~~sqqqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxqsqxxxxxxxxqssqqxxxxxL^^^L^^^^^xxxqs~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqDDDDDDDDrrsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqggqqs~~~~~~~~~~~~~~~ssqqqqsqqgqssqqsssqqgggggggg^^^^^^^gg^^^^^^^^^^^^^^^^^xgxx^!!^^xxxx^^^!!!!^^^^^^^^^^^^^^^^^ss~~~~~~~~~~sss^^^^^^^^^^^hhhLhh^^^^^^^^!!!!!!!!^!^!!!!!^^^!!!^^^^^xxxxLxxxxxxxx^^x^^!!^^^^^^^^^!!^!!!!^^^^xxxxxxqqs~~~~~~~~~ssss~~sqgggggqs~~sqqggpp^^!^^^^ppqs~~ssssssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddDDdddhhhppqqssss~~~~~~sqddddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxqssqxxxxxxqssqxxxxxxxLL^LLL^^^^xxxqs~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqDDDDDDqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qgggggggqsss~~~~~~~~sssssqggggqgggqsqggqqqggggggggg^!!^^!^^gg^^^^^^^ggggg^^^^gggxx^^^^xxxxx^^^^^!^^^^^xxxxx^^^^^ssss~~~~~~~~~~~~~s^^^^^hhh^hhhLLhh^^^!!!!^!!^^!^^^^^^^^^^!!^!^!!!^^^^xxxxxxLxxxxxxhh^^^^!^^^^^^^^^^^^^^!^^^^^^xxxxxxxxqs~~~~~~~~~~~~~~sqggggggqs~~sqggp^^!!^^p^pppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddDDDddhhhhhppqqqqs~~~~~sqddddDddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqssqxxxxxxqssqxxxxxx^^^^LLLL^^^^^xxqs~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqDDDDDDqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqggggggggqssss~~~~sqqqqsqgggg^^^^ggqqggggggggggg^^^^!^^^^ggg^^^gggggggggggggggggxgx^^^xxxxxxx^^^^^^^^xxxxxxx^^^^ss~~~~~~~~~~~~~~s~ss^hhhhhhhhLhhhh^^!!^!!!!^^^^^^^^^^^^^^^!!!!!!!!^^^hxxxxLxxxxxhhh^^^^^^^^^xxx^^^xxx^^^^^^xxxxxxxxxxqss~~~~~~~~~~~~~~~~qgggggq~~~sqggpp^!^^ppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddDDDDDDddhhhhppppppqs~~~~sqdDdDDdddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssssqxxxxxxqsqxxxxxxxx^^^LLV^^^^^xxxxqs~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qDDDqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggggggggqqssss~sqggggqggg^^^^^^^ggggggggggggg^^^!!^^gggggggggggggggggggggggggggxxx^^^xxxxxxxx^^^^xxxxxxxxxxxxqs~~~~~~~~~~~~~~~~~~~shhhhhhhLhhh^^^^!!!!!^^^^^^^^^^^^^^^^^^^!!!!!!^^^^hhxxLxxxhhhhh^^^^^^xxxxxxxxxxxx^^^^xxxxxxxxxxxqss~~~~~~~~~~~~~~~~~~qqggq~~~~ssqggp^^^ppqqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qdddDDDdDddphhphhhpppqss~~~~sqqdDDDddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxqsqxxxxxxxxx^^^^V^^^xxxxxxxqqss~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqggqgggggggqssssqgggggggg^^^^!!^^^^ggggggggggggg^^^^gggggggggggggggggggggggggggggxxxxxxxxxxxxx^^^xxxxxxxxxxxxxqs~~~~~~~~~~~~~~~~~~~~sshhhhhLhhhh^^^^^^!^^^^^^^^^^ss^^^^^^^^!!^^^!^^hhhhxxxLhhhhhhhh^^^^^xxxxxxxxxxxxx^^xxxxxxxxxxqqssss~sssss~~~~~~~~~~~~~qq~~~~~~ssqppp^^ppqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qddddDDDdddpppphhpppppqs~~~~~ssqdDdddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qxxxxxqsssqqxxxxxxx^^^^^^^xxxxxxxxxxqs~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqsqggggggqsssssqggggg^^^^^!!!!^^^gggggggggggggg^^gggggggggggggggqqgggggggggggggggxxxgxxxxxxxxxxxxxxxxxxxxxqqs~~~~~~~~~~~~~~~~~~~~~~sshh~LLhhhh^^^^^^^^^^^^^^sssssssssss^^^^^^^^^^^hhhhhhLhhhhhhhhhh^^^xxxxxxxxxxxxxxxxxxxxxxqqqsss~~ssqqqqqs~~~~~~~~~~~~~~~~~~~~~~sqppppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qdddddDDdppppppppppppqss~~~~~~qddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxqss~~ssqqxxxxxx^^^^^^xxxxxxxxxxq~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqggggggqss~~ssqqgggg^^^^^!!!!^^^ggggggggggggggggggggqqqqqqqqqqssqqqqqqggggggggggggxxxxxxxxxxxxxxxxxxxxxxqs~~~~~~~~~~~~~~~~~~~~~~~~~ss~shhhhhh^^^^^^^^^^^^s~~~~~~sss~ss^^^^^^^^^hhhhhhhhLLhhhhhhhhh^xxxxxxqqqxxxxxxxxxxxxxqsssss~~ssqxxxxxq~~~~~~~~~~~~~~~~~~~~~~~sqppppqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqddDDDddpppppppppppqs~~~~~~~sqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqss~~~~~~sqqxxxxx^^^^xxxxxqqxxqqs~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqggggqqss~~~~~ssqggggg^^^^^^!^^^gggggggggggggggqqqqqssssssssss~~ssss~sqqgggggggggxgxxxxxxxxxxxxxxxxqqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sshhhhh^^^^^^ssssss~~~~~~~~~~~~s^^^^^^^^hhhhhhhhhhhLhhhhhhxxxxxxqqqsssqxxxxxxxxxxxqsssssssssqqqxxxxqs~~~~~~~~~~~~~~~~~~~~~~~sqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddDDDdppppqpppqqqs~~~~~~~~~~~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~ssqxxxx^^^xxxxxxqsqqss~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggqss~~~~~~~~~sqgggggg^^^^^^^gggggggggggggggqsssss~~~~~~~~~~~~~~~~~~ssqggggqgggxxxxxxxxxxxxxxxxqqssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sshhhssssssssss~~~~~~~~~~~~~~~~s^^^^^^^hhsshhhhhhhLhhssqxxxxxxqssssssqxxxxxxxxxxqsss~ssqqqqxxxxxxxqs~~~~~~~~~~~~~~~~~~~~~~~~sssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqddDddqqqsqqqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxx^xxxxqqqs~s~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqgggqs~~~~~~~~~ssqgggqgggg^^g^^gggggggqqqqggqqs~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqsqqqqqxgxxxxxxxxxxxqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssss~sssss~~~~~~~~~~~~~~~~~~~sssss^^^sssshshsssLss~~sqqxxxqss~~sssqqqxxxxxxxqs~~~~sqxxxxxxxxxxxqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssddddqsssssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqs~~~~~~~~~~~ssqqqqggggggggggggggqqssssqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~ss~~ssssssqqxxxxxxxxxqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~ss^s~~~ss~s~~s~~~~~~~~qqxq~~~~~sqxxxxxxxxqqs~~~~sqxxxxxxxxxxxxqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqddddqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~~~~~~ssssqqqgqggggqqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqxxxxxxxqq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s~~~~~~~~~~~~~~~~~~~~~qs~~~~~sqxxxxxxxqss~~~~sqxxxxxxxxxxxqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qdddq~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qqxxxqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sssqsqqqqsss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxxxxqs~~~~~sqxxxxxxxxxxxqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssqxxxxxqs~~~~~~ssqxxxxxxxqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqxxxxqs~~~~~~~~sqxxxxxxxqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~qxxxxqs~~~~~~~~~sqxxxxqqs~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sqqqqs~~~~~~~~~~~sqqqqss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ssss~~~~~~~~~~~~~~~ss~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
